Michaelis wants one thing: to be accepted by the upper classes. And of course wanting that pretty much guarantees that it's never going to happen.
If he'd just accept his position, take his success, and be properly humble, Michaelis would be fine. But instead he wants Clifford and Clifford's friends to accept his as one of them. Ain't going to happen:
"[G]radually smart society realized that it had been made ridiculous at the hands of a down-at-heel Dublin street-rat, and revulsion came. Michaelis was the last word in what was caddish and bounderish." (3.6)
Only Connie feels any sort of sympathy for him. She realizes that he's unpleasant because people have been "unkind to him" (3.71-72), and he's incapable of making any sort of true connection. At heart, he's a "loose, isolated, absolutely lone dog" (4.1). And like a dog, he bites when he feels threatened. When Connie refuses his offer of marriage, he turns on her.
Mellors and Michaelis should be similar. They're both from lower class, poor backgrounds; they both have education and success beyond what they were born to. But they're complete opposites. The difference is that Michaelis has aspirations. He wants to be something he's not, so he ends up being dependent on other people, even if he doesn't want to be, even if "at the very bottom of his soul he was an outsider, and anti-social" (3.80). Mellors, on the other hand, is just himself. He's okay with people rejecting him or not liking him—he seriously just does not care.