If I was Tessio, I wouldn't want to be controlled by a much younger man than my own age. I would think I'm smart enough to run my own family now and Michael Corleone is still only a college kid, he doesn't have the sicilian balls or cunning to run the family right. Tessio was greedy as he probably wnated his own family now and didn't want to answer to Mike's command, also he thought Barzini would be able to take over the corleone empire when Vito dies.