Why are there so many sex determining systems in animals
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I don't quite know how to answer. I think that the only answer one could give is why not?. Various mechanisms may evolve under different life-history, different environment, different ecological strategy, different mutations occuring,..

In some species (including some amphibians) the evolution of sex determination system is highly dynamic and switch back and forth between one system and another.

I highly recommend the book: The Evolution of sex determination system (2014) that will give you a very good theoretical understanding of how sexual determination system evolve and make a complete review of empirical studies on the evolution and mechanisms of sex determination system. I think it is the only book existing on the subject.