As a dog returns to its vomit, so a fool repeats his foolishness.
Here is some good and penetrating commentary by Warren Wiersbe on this:
Fools don’t learn from their mistakes, but go right back to the same old mess. Experience is a good teacher for the wise but not for fools. This verse is quoted in 2 Peter 2:22 as a description of counterfeit believers who follow false teachers. Like a sow that’s been washed, they look better on the outside; and like a dog that’s vomited, they feel better on the inside; but they still don’t have the divine new nature. Consequently, they go right back to the old life. Obedience and perseverance in the things of the Lord are proof of conversion. Foolish tendencies in each of us are part of our sin nature. Recognizing them and depending on God’s remedies for these flaws are the first steps toward wisdom, forgiveness, and eternal life.
“This is eternal life: that they may know You the one true God, and the One You have sent-Jesus Christ .”
This, for me, is one of the most important verses in all of Scripture.
Here our Master defines for us eternal life. It’s not merely living forever. It is deeper than that. It changes our old understanding of John 3:16, enriching it, rendering it more tangible.
I defer to the eloquent A.W. Tozer for some exposition on this verse:
In religion more than in any other field of human experience a sharp distinction must always be made between knowing about and knowing. The distinction is the same between knowing about food and actually eating it. A man can die of starvation knowing all about bread, and a man can remain spiritually dead while knowing all the historic facts of Christianity. We have but to introduce one extra word into this verse to see how vast the difference between knowing about and knowing. “This is life eternal, that they might know about thee the only true God, and Jesus Christ, whom thou hast sent.” That one word makes all the difference between life and death, for it goes to the very root of the verse and changes its theology radically and vitally.
For all this we would not underestimate the importance of mere knowing about. Its value lies in its ability to rouse us to desire to know in actual experience. Thus knowledge by description may lead on to knowledge by acquaintance. May lead on, I say, but does not necessarily do so. Thus we dare not conclude that because we learn about the Spirit, we for that reason actually know Him. Knowing Him comes only by a personal encounter with the Holy Spirit Himself.