Prove that a set cant be a element of itself.

I have spent hours researching this but i simply cant understand how this is impossible! How can the fact that something is true make it false? I seriously just cant understand this concept.

Online i keep getting people referencing " the Axiom of Regularity" etc. and Honestly this is adding to my confusion.

so if you want to help, please try not to make reference to other theorems, but if it is absolutely necessary please also add a proof for the theory.

lastly please provide maths with English explanations.

thanks to anyone that is willing to help !