Michael's hostility to Tom arose from a kind of sibling rivalry. His resentment was shown as early in time as the
attack on Pearl Harbor (which was 5 years before The Godfther). When Tom tells Michael that his father had pulled strings to keep him out of the military, Michael is seething, then when Tom says something about how he and Vito had big plans for him Michael says "You discuss My future with MY father." It is not so much a question or an observation but an objection that Tom had the right to talk to Vito about him.

Michael's hostility played right into Tom's yearning tobe thought of as a "real brother, " so Michael killed two birds with one stone........three really, because this kept Tom under Michael's thumb, which was necessary because other than Michael Tom knoe more about the family business than anyone.