I think there's a big difference in really believing in an issue, pushing it whenever it comes up, and then changing your mind and saying "forget I said anythin

I think there's a big difference in really believing in an issue, pushing it whenever it comes up, and then changing your mind and saying "forget I said anything", versus really believing in that issue, and then changing your mind and explaining why you changed your mind, putting effort in correcting your earlier mistake, and now putting at least as much effort in the better side of the issue. The latter is a convincing change of mind. The former looks more like abandoning a feebly held belief.