I do the same thing and I am not at all comfortable in saying I was wrong if I was, but I generally do it anyway because, well, fair is fair and I was indeed wrong plus I better than I discover it and correct it that keep on spouting bullshit.

That said, if the other person was an assholein our discussion (for example, using personal attacks and insults) I won’t openly admit to them that I was wrong as I don’t want to give them the satisfaction (though I’ll internally accept I was wrong and correct my take from there oewards).