I am a math PhD student considering changing universities. I have suspicions that my supervisor has not been very honest with me since I told him that I considered changing universities (and therefore supervisors) because of shift in interests. He got angry with me, told me that it would bring bad reputation to the research group and that I can't just leave after 1 year.
In a conversation I mentioned a university, in which there is a professor, call him professor M, whose work interests me. My supervisor said that professor M is the only one in his field in the university (apparently with the intent of discouraging me from trying to apply to that university). I looked up the website of professor M's research group, which seems to tell a different story (plenty of PhD students, at least one post doc). I found this a bit suspicious. Moreover I recently realized that my supervisor has coathored an article with an emeritus professor, who is in the university, who has worked on the same field, although not part of the research group of M. The "research group" in my university is not that active itself.
When I told him that I want to consider alternatives he told me that the doctoral programme is collecting information about PhD students (which was true), and that he needed to know whether I was part of the group or not. He gave me 3 days to decide whether to stay or leave the doctoral program. I asked the coordinator of the program about this, and he told me that the list in question changes all the time and that it is not nearly as serious matter as my supervisor claimed. It should be noted that my supervisor is notoriously bad at bureucratic/adminstrative university matters.
I suppose in all the above cases it is possible that the explanation is something less malicious, such as ignorance or misunderstanding. In any case I am not in good terms with my supervisor and I don't think we trust each other very much.
The dilemma is that the funding is good and secured, and that the alternatives are abroad (and uncertain).
Could the situation be worth fixing? Should I run for my life? Is there a risk that if I try to change universities he will refuse to write a recommendation letter or write a mild one (he supervised my Master's thesis)?