Can Socrates refute himself?

I suppose he could, if he changed his argument or came up with new evidence or arguments that refuted the old one.

If one of his claims refutes the other, then clearly, at least one of them is wrong, and the other may or may not be right.

It isn't about truth, it's about the search for truth. Accepting anything as right or true ultimately and without any room for review, defeats the purpose of searching for that truth in the first place. To search, one must be open-minded and always questioning.

He was right when he refuted himself. He had second, truer thoughts.

Because of lack of ego, even though he tried to do it, he could not succeed.

Philosophically speaking, this is our confusion, but not that of Socrates.

He's really clever, that's how.

can a rabbit pull a hat out of its butt

Ah, he died in 399 BC so, I don't think so.

He did not seek to be right.

He's dead now, so no.

why would he?