Question: Doesn't the Bible teach that we can lose our salvation?

Question: I’m confused about the “security of the believer.” To me, it sounds like “once saved, always saved,” which doesn’t fit in with my understanding that believers can lose their salvation by turning their backs on God. 

Response: The doctrine of “Eternal Security” engenders no end of strife. But a discussion of the pertinent scriptures must be according to 2 Timothy:2:15Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth.
See All..., in which we are told to “rightly divide the word of truth.” Everything must be considered in context. The passage in John 10 contains declarative statements of the Lord Jesus Christ, with no qualifiers. Jesus made five clear statements concerning His sheep (those who believe and follow Him), in contrast to those who did not believe (v. 26). Some defenders of the “falling away” doctrine try to draw a distinction between Christians who continue to follow Jesus throughout their lifetimes and those who eventually turn back.

Jesus, however, shows that He was making a simple distinction between the Pharisees who did not turn to Christ and those who did (vv. 24-26). The verses put the security of eternal life in the strong right arm of God. The verse says “no man may pluck them out.” The good shepherd recovering his lost sheep (Mt 18:12-14) and the Father disciplining His children (Heb:12:5-12 [5] And ye have forgotten the exhortation which speaketh unto you as unto children, My son, despise not thou the chastening of the Lord, nor faint when thou art rebuked of him: [6] For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth. [7] If ye endure chastening, God dealeth with you as with sons; for what son is he whom the father chasteneth not? [8] But if ye be without chastisement, whereof all are partakers, then are ye bastards, and not sons. [9] Furthermore we have had fathers of our flesh which corrected us, and we gave them reverence: shall we not much rather be in subjection unto the Father of spirits, and live? [10] For they verily for a few days chastened us after their own pleasure; but he for our profit, that we might be partakers of his holiness. [11] Now no chastening for the present seemeth to be joyous, but grievous: nevertheless afterward it yieldeth the peaceable fruit of righteousness unto them which are exercised thereby. [12] Wherefore lift up the hands which hang down, and the feeble knees;
See All...) are excellent examples of God securing our salvation. Other people argue that in John 10 some have added meanings that do not agree with the words or the context of the passage in John. Perhaps the clearest example is 2 Peter:2:22But 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..., which discusses false prophets, not true believers. These “false prophets” (2:1) are “wells without water (v. 17).” A well without “water” (water is biblical metaphor for the Holy Spirit) has the same exterior appearance as a bona fide well but looks entirely different to one who possesses the ability to look inside (1 Sm 16:7). These false prophets are specifically contrasted with Lot who, despite his compromises and disobedience, is still called a “righteous man” (v. 8). As verse 22 carefully explains: “…it is happened unto them according to the true proverb….” Another verse cites the dog that returns to his vomit because that’s what dogs do. The sow returns to wallowing in the mire because that’s what a hog does. Neither the dog nor the pig has had its nature changed. Nor were they “born again” or changed into another species. The dog experienced a temporary purging and the sow underwent a washing. But there was no eternal meaning, even with spruced up appearances—like the whitewashing of a tomb (Matthew:23:27Woe unto you, scribes and Pharisees, hypocrites! for ye are like unto whited sepulchres, which indeed appear beautiful outward, but are within full of dead men's bones, and of all uncleanness.
See All...).

Those who have been drawn by Christ (who draws all men [John:12:32And I, if I be lifted up from the earth, will draw all men unto me.
See All...]), may temporarily “escape” the pollution of the world by attempting to conform, but Scripture plainly states that their conformity is not real because their true nature (as that of a dog or pig) soon manifests itself.