Can a person lose their salvation according to 2 Peter 2:20-22?
The short answer is "Yes, most definitely."
The following response may be unpalatable to some. However, it is certainly not my intent to wound those who believe we simply cannot be lost once we receive salvation in Christ. The far greater imperative here is for the truth to be told, that which surpasses any sensitivities of those who may disbelieve it.
It is to the misinterpretation of passages like that of the OP which I speak.
I would like to point out several instances where we are told that someone can, indeed, fall away from the faith. And, in doing so, they are in a perilous condition.
1. In the Gospel of John, Jesus proclaimed:
John 15:2, 6: “Every branch in Me that does not bear fruit, He takes away; and every branch that bears fruit, He prunes it so that it may bear more fruit."
6“If anyone does not abide in Me, he is thrown away as a branch and dries up; and they gather them, and cast them into the fire and they are burned" (emphasis added).
Is Christ not warning his disciples that anyone who does not abide in Him -- that is, in all His commandments, will be "gathered and cast into the fire where they are burned"? Is that fire not Hell? How else can we read this? Is someone who accepted Christ and was baptized only to later decide to lead the life of an unrepentant criminal still saved? Has this person not, as with the OP's verses, metaphorically returned to "his own vomit" to "wallow in the mire"?
2. In Paul's Letter to the Galatians, the apostle warned that if these Christians continued to abandon their faith in favor of the Law of Moses, the Gospel would be useless:
Galatians 5:2: "Behold I, Paul, say to you that if you receive circumcision, Christ will be of no benefit to you" (emphasis added).
If Christ is "of no benefit" to Christians who looked back to the Old Law, how then can they be spared from eternal separation with God? This is followed by another stern warning from Paul:
Galatians 5:4: "You have been severed from Christ, you who are seeking to be justified by law; you have fallen from grace" (emphasis added).
Is it possible to ignore the words "severed from Christ" and "fallen from grace"? How can we be "severed from Christ" if we were never "in Him" in the first place? And, if we are severed or have fallen from Christ, does this not mean we are lost in eternal flames? Is there some "safety net" that will still catch the ex-Christian as they plunge headlong into Hell? If these admonitions are unconvincing, just what will ever convince someone that yes, we can fall away from the faith?
3. Perhaps the "go to" Book of the Bible in the matter of apostasy is the Letter to the Hebrews. There, we read several grave warnings:
Hebrews 2:1-3: For this reason we [Christians] must pay much closer attention to what we have heard, so that we do not drift away from it. For if the word spoken through angels proved unalterable, and every transgression and disobedience received a just penalty [in the O/T], how will we escape if we neglect so great a salvation [in Christ]?"
This passage is asking, if we "drift away" from the faith which we now possess, how will we escape the wrath of God? If I decide to denounce -- for life -- my Christianity, have I not "drifted away" from (indeed, jettisoned) my faith? If not, how so? Are we to actually believe that God will refuse my denunciation?
4. Again, in the Letter to the Hebrews, we are cautioned never to develop faithlessness:
Hebrews 3:12: "Take care, brethren [Christians], that there not be in any one of you an evil, unbelieving heart that falls away from the living God" (emphasis added).
From this verse, the clear implication is that we can develop an evil, unbelieving heart that **falls away from God." And, if we do this, we will never enter into paradise with Him. It seems to me that to believe otherwise constitutes a certain spiritual blindness.
5. Later, in chapter 6 of the same Letter we read:
Hebrews 6:4-6: "For in the case of those who have once been enlightened and have tasted of the heavenly gift and have been made partakers of the Holy Spirit, and have tasted the good word of God and the powers of the age to come, and then have fallen away, it is impossible to renew them again to repentance, since they again crucify to themselves the Son of God and put Him to open shame" (emphasis added).
If the clause of verse 6 above ("then have fallen away") does not mean what it says, how then do words have meaning? Clearly, this passage is speaking of those who received the Gospel. They "were made partakers of the heavenly gift [of Christ]," and have "fallen away" from Him. The writer then warns that it is impossible for someone in this state to be renewed as long as they persist in their present, fallen condition. Obviously, then:
Hebrews 6:8: "[If this person] yields thorns and thistles [produces worthless fruit to God], [they are] worthless and close to being cursed, and end up being burned."
How is someone in such a condition saved? Can we really employ textual contortions to somehow modify the meaning of the text? Or is it not the case that when someone turns to a life of willful disobedience, they are "putting the Son of God to open shame" (6:6)? As chapter 10 of the same Letter explains:
Hebrews 10:26-27: "For if we go on sinning willfully after receiving the knowledge of the truth, there no longer remains a sacrifice for sins, but a terrifying expectation of judgment and THE FURY OF A FIRE WHICH WILL CONSUME THE ADVERSARIES" (cf. Isa. 26:11, 1 Thess. 1:7, emphasis added).
There should be no doubt that if someone falls away from their faith in Christ, there is no longer any sacrifice for their sins unless they return to Him. All that is left is "a terrifying expectation of judgment."
6. Too often, we rely on the advice of those who seem to casually dismiss biblical texts of the clearest import. Everyone should understand the meaning of 2 Peter 2 in the OP:
2 Peter 2:20-22: "For if, after they have escaped the defilements of the world by the knowledge of [Christ], they are again entangled in them and are overcome, the last state has become worse for them than the first… It has happened to them [apostates] according to the true proverb, “A DOG RETURNS TO ITS OWN VOMIT,” and, “A sow, after washing, returns to wallowing in the mire” (emphasis added).
Those who fall away from the faith are in a much more severe state than they were before they received Christ in the first place. I suggest the text of 2 Peter 2 could not be clearer in this regard.
These passages only scratch the surface of the truth that saints can fall away. We should ask ourselves -- not based on someone else's opinion, -- not what we have been told, but rather on our own eyes: How do these passages (and many more) not speak directly to those who have received the gift of grace from God, and have then forsaken it? Is such a person, unrepentant in their denunciation of God, really saved whatsoever? If so, how?
It is truly a wonder that anyone cannot see this obvious "forest" for the trees.