One of many problems with attempts to explain why the Master is evil is that it was already done all the way back in Colony in Space in 1971, and no later explanation has come close to matching that initial version in my opinion.
Colony in Space is a rather dull serial with plenty of plotting issues, but the whole thing is worthwhile for that one scene where the Master offers the Doctor joint rule of the universe and tries to get him to see his point of view. The Master’s motivations are encapsulated perfectly in lines like “one must rule or serve—that’s a basic law of life”, without any need to appeal to outside influences like drums or Death or even insanity. Colony in Space rightly portrays the Master as someone who seeks power over everyone else because they genuinely think they deserve it. It shows that the Master believes the only two choices life has to offer are to be master or servant, and they absolutely refuse to be the latter.
The ethical debate the Master has with the Doctor in this serial is far, far more compelling than any of the later attempts to explain Master’s evilness.