Position One: The eternal security of the believer. John 10:28-29 states that believers cannot be plucked from the hand of God. Luke 10:20 says that believers' names are written in heaven. Ephesians 1:13 adds that believers are sealed with the holy Spirit of promise. And, Ephesians 2:8-9 speaks of salvation as an act of grace and is the gift of God.
Position Two: Can lose salvation. Hebrews 10:26-31 maintains that believers who willfully sin after knowing the truth have trampled the sacrifice of Jesus and will fall into the hands of the living God. Second Peter 2:20-22 declares that if a believer becomes entangled in the world after knowing Jesus, it is far worse for them and they would have been better off to not known the way of righteousness. Matthew 7:21-23 reveals that not every one that says, "Lord, Lord", will enter into the kingdom of heaven. Galatians 5:4 asserts that believers can fall from grace.
There's more verses, to be sure, but these seem to be the biggies. But, there seems to be three verses that both views claim. It's Hebrews 6:4-6. The verses are too long to enumerate here. Side One infers that Paul is talking to immature believers and is telling them that it's impossible to "fall away" so long as they're continuing to grow spiritually. It's a warning that once one has tasted the milk, he/she must continue to grow in the faith. Side Two takes the same verses and says that it's impossible for a believer who has fallen away to be renewed again.
Same three verses and two completely opposite understandings. The Book of Hebrews is a difficult read. The challenge it presents is a good one. Studying this particular passage should, indeed, encourage a pursuit of what the message really is. Hopefully, for those who pursue it's meaning, it will lead to enlightenment, a tasting of the heavenly gift and partakers of the Holy Ghost.
Whichever side of this fence you stand one, one thing is sure. If you follow Jesus and "endure to the end," your soul can always rest in His peace.