I believe in eternal security. However, a co-worker recently presented me with the following scriptures and asked me to explain eternal security with these in mind. Hebrews 6:4-12 [4] For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost, [5] And have tasted the good word of God, and the powers of the world to come, [6] If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame. [7] For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God: [8] But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned. [9] But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak. [10] For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name, in that ye have ministered to the saints, and do minister. [11] And we desire that every one of you do shew the same diligence to the full assurance of hope unto the end: [12] That ye be not slothful, but followers of them who through faith and patience inherit the promises.
See All... and 10:26
See All...; 2 Peter 2:20-22 [20] For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning. [21] For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them. [22] But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.
See All... and 3:14-17 [14] Thou didst strike through with his staves the head of his villages: they came out as a whirlwind to scatter me: their rejoicing was as to devour the poor secretly. [15] Thou didst walk through the sea with thine horses, through the heap of great waters. [16] When I heard, my belly trembled; my lips quivered at the voice: rottenness entered into my bones, and I trembled in myself, that I might rest in the day of trouble: when he cometh up unto the people, he will invade them with his troops. [17] Although the fig tree shall not blossom, neither shall fruit be in the vines; the labour of the olive shall fail, and the fields shall yield no meat; the flock shall be cut off from the fold, and there shall be no herd in the stalls:
See All... What is your viewpoint?

We already have articles on the site about Hebrews 6:4-12 [4] For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost, [5] And have tasted the good word of God, and the powers of the world to come, [6] If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame. [7] For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God: [8] But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned. [9] But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak. [10] For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name, in that ye have ministered to the saints, and do minister. [11] And we desire that every one of you do shew the same diligence to the full assurance of hope unto the end: [12] That ye be not slothful, but followers of them who through faith and patience inherit the promises.
See All... and Hebrews 10:26For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins,
See All.... Perhaps you can check them out.  2 Peter 2:20-22 [20] For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning. [21] For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them. [22] But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.
See All... and 2 Peter 3:14-17 [14] Wherefore, beloved, seeing that ye look for such things, be diligent that ye may be found of him in peace, without spot, and blameless. [15] And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you; [16] As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction. [17] Ye therefore, beloved, seeing ye know these things before, beware lest ye also, being led away with the error of the wicked, fall from your own stedfastness.
See All... are passages that show the possibility of people failing from the truth of the gospel and from true faith in Christ. There are many scriptures that show this possibility.

The key is to understand that those who can go right back to the old ways without any change were probably never true believers in the first place. This is a tricky subject, since the Bible does teach the possibility of true believers going through a time of backsliding. However, God assures us that true believers who backslide will be beset with the chastening hand of God and will never be able to rest in their backslidden condition. "For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth" (Hebrews 12:6For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth.
See All...).  

But we are also given another picture. 1 John 2:19They went out from us, but they were not of us; for if they had been of us, they would no doubt have continued with us: but they went out, that they might be made manifest that they were not all of us.
See All... states, "They went out from us, but they were not of us; for if they had been of us, they would no doubt have continued with us: but they went out, that they might be made manifest that they were not all of us." This passage shows us that some return to their old ways as proof that they were not true believers in the first place. See how this truth fits in with 2 Peter 2:20-22 [20] For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning. [21] For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them. [22] But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.
See All....    

2 Peter 2:20For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning.
See All... For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning.  21 For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them.  22 But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.  

Notice the conclusion. They are as dogs who return to their own vomit or as sows (pigs) who return to the mire (the pig pen). God's people are never compared to dogs or pigs. They are sheep. But these people are still pigs (or dogs). They have never become sheep. Yes, they escaped the pollutions of the world for a time by learning the ways of Christ and reforming their actions. They knew the way of righteousness as a set of facts can be memorized. But they did not know God in their hearts. They were still pigs. And, when they return to the world, their latter end will be worse than the beginning. They will fall even deeper into sin.  

This condition is illustrated by the man who was rid of the evil spirit in Matthew 12:43-45 [43] When the unclean spirit is gone out of a man, he walketh through dry places, seeking rest, and findeth none. [44] Then he saith, I will return into my house from whence I came out; and when he is come, he findeth it empty, swept, and garnished. [45] Then goeth he, and taketh with himself seven other spirits more wicked than himself, and they enter in and dwell there: and the last state of that man is worse than the first. Even so shall it be also unto this wicked generation.
See All.... When the evil spirit returned to the man, he found his house "empty, swept, and garnished." Because of this, he found seven other spirits "more wicked than himself" to enter and dwell in the man. So, "the last state of that man is worse than the first." The problem occurred because the man experienced reformation without regeneration. His heart was swept, but it was also empty. He cleaned up his life, but he did not have the indwelling Christ.  

2 Peter 3:14-17 [14] Wherefore, beloved, seeing that ye look for such things, be diligent that ye may be found of him in peace, without spot, and blameless. [15] And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you; [16] As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction. [17] Ye therefore, beloved, seeing ye know these things before, beware lest ye also, being led away with the error of the wicked, fall from your own stedfastness.
See All... is dealing with the same problem. However, here Peter urges them to make sure of their salvation. We find similar exhortations in other places. 2 Corinthians 13:5Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?
See All... states, "Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?" Reprobates are those rejected from salvation (see Jeremiah 6:30Reprobate silver shall men call them, because the LORD hath rejected them.
See All...) because they have never truly received Christ. They are "reprobate concerning the faith" (2 Timothy 3:8Now as Jannes and Jambres withstood Moses, so do these also resist the truth: men of corrupt minds, reprobate concerning the faith.
See All...). They are "led away with the error of the wicked" (2 Peter 3:17Ye therefore, beloved, seeing ye know these things before, beware lest ye also, being led away with the error of the wicked, fall from your own stedfastness.
See All...). We must "be diligent" (2 Peter 3:14Wherefore, beloved, seeing that ye look for such things, be diligent that ye may be found of him in peace, without spot, and blameless.
See All...) and "beware" (2 Peter 3:17Ye therefore, beloved, seeing ye know these things before, beware lest ye also, being led away with the error of the wicked, fall from your own stedfastness.
See All...) lest we find ourselves in that number.