I really want to say because Frey and Henley(especially Frey) were too full of themselves. The prevailing answer is that Meisner was struggling with a lot of issues(mental and maybe otherwise) and he wanted to slow down a bit and he was getting tired of singing Take It To The Limit all the time. So Frey basically either did the ultimatum or plain kicked him out
Edit: I'm not a very big Eagles guy
And when Alexander saw the breadth of his domain, he wept for there were no more worlds to conquer"
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