How to make the villain's motives understandable if his logic is flawed?

In a story I'm writing, the villain has his motives for his attitudes.
However, he is very mentally disturbed, which makes the logic of his motives be kind of illogic to other people (including the reader).

So how to make the reader find understandable the villain's motives even if it's illogic?

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How to make the villain's motives understandable if his logic is flawed?

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