In the scene referenced above, Benedick is claiming that "he did not think he would live till he was married." He is claiming that he didn't actually change his mind, he just lived longer than he thought he would. In other words, Benedick is still suggesting that he has been right all along.
However, in the last scene, Benedick finally owns up. He says "man is a giddy thing", meaning that man is often foolish and says things that he doesn't mean. He has recognized the joy that shall come with marriage, and embraces it as he has always embraced his beliefs.
In Act II, scene 3, Benedick overhears Don Pedro, Leonato, and Claudio's staged discussion of Beatrice's love for him. He then admits his love for her, and rationalizes it this way:
"I may chance have some odd quirks and remnants of wit broken on me, because I have rail'd so long against marriage. But doth not the appetite alter? A man loves the meat in his youth that he cannot endure in his age. Shall quips and sentences and these paper bullets of the brain awe a man from the career of his humor? No, the world must be peopled. When I said I would die a bachelor, I did not think I should live till I were married."
This is one of the most comic scenes in the play because Benedick's attitude changes so quickly and so violently.