I would echo Lou's words, but perhaps somewhat differently, and just pose the question:

Why would anyone take what Oswald said at face value and just say: "Case closed. If he says he didn't do it, he must not have done it."

Hitler promised Chamberlain in 1938 that he wouldn't invade Poland. How did that work out? People say things they don't mean all the time, for any number of reasons and sometimes for no reason at all.

It would be pointless to try figure out the reasons why unreasonable people would do what they do. Even if you got the explanation out of him, it might not make any sense, as with Mark Chapman. Oswald was obsessed with the idea of becoming a well known figure, to the point that upon returning to the United States following his defection to the USSR his first question to his brother Robert was: "where are the reporters?" hoping that a mob of press would be there to ask him why he had returned. According to Robert Oswald, Lee was disappointed to make the realization that nobody cared.

Only six months earlier he had tried to (and came close) to assassinating General Edwin Walker, with the same purpose in mind. The idea that he would martyr a public figure was a thought he had been entertaining for some time.