"Oswald was extremely critical of President Kennedy, and he was just obsessed with what America did to support this invasion at the Bay of Pigs.... obsessed with his anger towards Kennedy...."
Volkmar Schimdt, relating a conversation he had with Oswald at a party in Dallas in February of 1963.
I find it difficult to believe that a self-described Marxist (as he understood the word) who admired Castro so much that he actually sang songs to him would also admire the president of the main enemy of that man. It makes no sense. Yes, we have DeMohrenschildt saying that Oswald "admired" JFK and Marina saying she thought he "liked" Kennedy. So one can argue it both ways.
But let's remember that Oswald "left" the Texas Schoolbook Depository Building about three minutes after the shooting. There is no evidence that at any time afterwards did he show any interest at all in what happened to Kennedy, the man he supposedly "like" or "admired." He never talked to any co-worker about the incident, he didn't stay around to find out what happened to Kennedy, he never discussed with anyone he met on his way to his rooming house the incident and when he arrived at his rooming house to discover the housekeeper watching television he never once asked her if she knew what happened.
Zero interest at all. For a politically obsessed person like Oswald that is very, very odd.