Alceste seems to like saying that he is not a reasonable guy. It's a kind of weird thing to say about yourself, but in Alceste's case it is also true. He says, "Enough of reasoning, now. I've had my fill," and, "True, true: each day my reason tells me so;/ But reason doesn't rule in love, you know," and even, "Sir, you're a matchless reasoner, to be sure;/ Your words are fine and full of cogency;/ But don't waste time and eloquence on me./ My reason bids me go, for my own good" (1.1.184, 1.1.259, 5.1.91).
OK, fine. But what exactly is Alceste's "reason"? Our protagonist is not exactly a calm guy, and if he isn't ruled by reason then he must be ruled by his emotions. It makes sense—he's always yelling, crying, begging, doing something over the top and emotional. On the other hand, there's Philinte, who is the epitome of a calm reason.
So maybe Molière is trying to tell us that reason and love, or reason and absolute sincerity, are incompatible. Or maybe he was just trying to make Alceste funny.