Yes you admitted your mistake. And yes you still acted a bit foolish. That’s not a false accusation, it’s just an accusation.

(THIS is an example of an opinion)

Can you just take a second to reflect on how inelegantly you have taken being wrong? You made an incorrect assertion of a fact, just accept you made a mistake and move on. Being stubborn and defensive makes you look kind of immature.

Hope you can take this advice