The speaker of "The Flea" is a smart aleck who will never admit to having lost an argument. You could catch him in some ridiculously absurd conclusion, and he would be like, "A-ha! But that just proves that this other thing I said was right!" And then you would go: FACEPALMS. In this poem, for example, he changes his argument a couple of times. At first he claims that falling for his charms won't cause his beloved any shame. Then he says it's too late to worry about shame because they are already married. Then he accuses her of attempted murder. Then this argument is exposed as a fraud, which he thinks proves the first argument. Etc., etc. All in a day's work for a seducer.
Interestingly, the speaker also seems to be a devout Christian, or at least he wants the woman to think he is. He uses religious imagery, including allusions to Jesus Christ and the Trinity, to argue that killing the flea would be a horrible sin. He talks a lot about the sanctity of marriage, probably because he wants to convince her that he's an honorable gentleman, not someone looking for a one-night stand. He has a lot of work to do on that front, because apparently neither her parents nor the woman in question have much interest in their marriage. In other words, he's probably not some gorgeous prince with three estates and a lot of fancy paintings. His greatest wealth is his capacity for language.