What might make Mueller hate Trump? (Besides the fact that he apparently applied to get back the job of FBI Director, and didn't get it).
1. Lawyer. As Tocqueville says, lawyers are in a way conservative: they trust established laws and precedents more than anything totally new. What is new can persuade them if it is dressed in old language, and of course if it favours groups close to their hearts. Supreme Court decisions have to at least pretend to be based on the text of the Constitution, and on at least some precedents, at least some of them somewhat old. In some cases the efforts to keep up this appearance are tortuous, but that's lawyers for you. Family law: it's crazy for so many issues to become adversarial, winner take all, but it's good for lawyers, and they keep up the appearance that sacred rights are being protected. Copyright, including movies, is starting to seem old-fashioned; Disney got Congress to grant a ridiculous extension on Snow White, etc. When Walt Disney made the movies, the stories were in the public domain. Now Disney claims the only version anyone knows is the Disney version, so it deserves to be protected.
It may be that lawyers in general have tended to hate Trump: his speaking from the hip, apparent impetuousness or failure to think before he speaks/tweets (some of which may be strategic), his open contempt for judges and sometimes laws. Some of this could be almost tailor-made to infuriate lawyers.
2. Credentials: Mueller a decorated Marine, a graduate of good schools, he has had periods in private practice so it has perhaps never been true of him that he has no real choice, in the income bracket in which he wishes to be, but public service. Trump, as he has been known to say, graduated from better schools than many journalists, with better grades, but he almost makes a point of talking like some kind of New York dock worker, holding forth in his favourite bar. He sometimes seems to be the kind of poorly-informed loudmouth Mueller has trained himself not to be. If Trump succeeds, he at least raises the question why anyone needs fancy credentials. Who would prefer Jeb, or perhaps any member of the Bush family other than (the elder) Barbara, to Trump? I think there has always been a bias against electing entrepreneurs, successful or not, to high office. They succeed by looking narrowly at the bottom line; if they have dreams, achieving those dreams may involve ruthlessly harming the interests of weaker or less far-seeing people. Does Trump suggest an entrepreneur can do a good job, even if he's not a gentleman?
3. Bureaucrat. Mueller and Comey spoke out on some issues, with at least some cover from other bureaucrats, in the Bush Junior years. Otherwise they seem to have defended the FBI line on things: defending questionable convictions that are later overturned, etc. I don't think anyone thinks Trump would have lasted five minutes as a bureaucrat.