Let's examine the text to which you refer.
For if, after they have escaped the pollutions of the world through the knowledge of the Lord and Savior Jesus Christ, they are again entangled in them and overcome, the latter end is worse for them than the beginning.This text gives insight into Christians who fall back into sin and are overcome by sin. Being overcome by sin means they do not want to repent and make things right with God.
For it would have been better for them not to have known the way of righteousness, than having known it, to turn from the holy commandment delivered to them. But it has happened to them according to the true proverb: "A dog returns to his own vomit," and, "a sow, having washed, to her wallowing in the mire."
(2 Peter 2:20-22 NKJ)
They have decided to go their own way. They eventually turn from the holy commandment, which is believing on the Lord Jesus Christ (1 John 3:23).
When Christians do this, the Bible reveals, "Their latter state becomes worse than their beginning state." They end up being a worse sinner and having more problems than before they met the Lord and He delivered them. When this happens, it is like a dog returning and eating its vomit or a pig going back into the mud after being washed.
The most important aspect of this section of Scripture is the realization that Christians have to live holy lives and not toy with sin.
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