Eternal Security vs. the Bible
The New Testament clearly supports Catholic soteriology and the possibility of apostasy.
Hebrews 6:4-6 (RSV) For it is impossible to restore again to repentance those who have once been enlightened, who have tasted the heavenly gift, and have become partakers of the Holy Spirit,  and have tasted the goodness of the word of God and the powers of the age to come,  if they then commit apostasy, since they crucify the Son of God on their own account and hold him up to contempt.
This is one of the very best texts against eternal security. This passage is referring to (as I see it, anyway), blasphemy against the Holy Spirit, which is indeed unforgivable; but that doesn’t cover all cases of apostasy. Other cases may involve a person returning to the faith. Some Protestant commentators and apologists argue that the passage is merely rhetorical or hypothetical.
I don’t see that it reads that way at all. It’s talking about real people: “those who have once been enlightened, who have tasted the heavenly gift, and have become partakers of the Holy Spirit” and it refers to them literally committing what we are saying is a real and distinct (and terrifying) potentiality: “they then commit apostasy.”
Hypothetical rhetoric does indeed occasionally occur in Scripture. Perhaps the most famous example is the following passage from St. Paul:
1 Corinthians 15:12-20 Now if Christ is preached as raised from the dead, how can some of you say that there is no resurrection of the dead?  But if there is no resurrection of the dead, then Christ has not been raised;  if Christ has not been raised, then our preaching is in vain and your faith is in vain.  We are even found to be misrepresenting God, because we testified of God that he raised Christ, whom he did not raise if it is true that the dead are not raised.  For if the dead are not raised, then Christ has not been raised.  If Christ has not been raised, your faith is futile and you are still in your sins.  Then those also who have fallen asleep in Christ have perished.  If for this life only we have hoped in Christ, we are of all men most to be pitied.  But in fact Christ has been raised from the dead, the first fruits of those who have fallen asleep.
Note that the logical structure is of this form:
“If x isn’t true, neither is y; if y is untrue, then so is z” (15:13-14 and repeated in 15:16-17)
“If x is untrue, we are of all men most to be pitied” (15:19)
“But in fact, x is true, and therefore, so are y and z” (15:20)
Paul makes very clear (leaving no doubt) what he is doing, by saying “if there is . . . ” and using the word “if” over and over, signifying a hypothetical word-picture. But then he counters that by saying “in fact” in verse 20.
Hebrews 6:4-6, in contrast, is not at all like that. It has neither the required structure nor all the “ifs” to suggest that it is merely hypothetical. The argument for Hebrews 6:4-6 fails, and as the old saying would have it: “you can’t make a silk purse out of a sow’s ear.”
To top it off, the writer of Hebrews once again shows that perseverance (as opposed to instant assurance) is always part of the overall picture:
Hebrews 6:11-12 And we desire each one of you to show the same earnestness in realizing the full assurance of hope until the end,  so that you may not be sluggish, but imitators of those who through faith and patience inherit the promises.
2 Peter 2:20-21 For if, after they have escaped the defilements of the world through the knowledge of our Lord and Savior Jesus Christ, they are again entangled in them and overpowered, the last state has become worse for them than the first.  For it would have been better for them never to have known the way of righteousness than after knowing it to turn back from the holy commandment delivered to them.
This is one of the very best indications of Catholic soteriology and the possibility of apostasy. Some Protestants, unfortunately, resort the time-honored technique of redefining words, in order to bolster an erroneous view that this is not referring to apostasy. They claim that “knowledge of our Lord and Savior Jesus Christ” is not a saving knowledge. It’s merely (so we are told) a non-salvific head knowledge.
The problem with that is the preceding clause: “they have escaped the defilements of the world through ... ” Only God’s grace offers such an escape. So they were indeed in God’s graces (as Catholics would say), or “saved” (as Protestants would describe it).
Moreover, 2 Peter 1:3 uses the same word “knowledge” (the same Greek word, epignosis) in (undeniably) the sense of saving knowledge. St. Peter uses this Greek word repeatedly in this sense:
2 Peter 1:2 May grace and peace be multiplied to you in the knowledge of God and of Jesus our Lord.
2 Peter 1:8 For if these things are yours and abound, they keep you from being ineffective or unfruitful in the knowledge of our Lord Jesus Christ.
The same word is used four times, yet we are to believe that it means something much different in 2 Peter 2:20? This is classic eisegesis (wrongly reading into the Bible what isn’t in fact there). St. Paul also uses the same word, epignosis, in the same sense, 13 times (Romans 10:2; Ephesians 1:17; 4:13; Philippians 1:9; Colossians 1:9-10; 2:2; 3:10; 1 Timothy 2:4; 2:25; 3:7; Titus 1:1; Philemon 6), and never for mere head (non-saving) knowledge.
Here are additional biblical passages along these lines: 1 Samuel 18:12; Ezekiel 18:24; 33:12-13, 18; 1 Corinthians 10:12; Galatians 4:9; Philippians 3:11-14; Colossians 1:22-23; 1 Timothy 4:1; 5:15; Hebrews 3:12-14; 12:15; 2 Peter 2:15; Revelation 2:4-5.