Admitting Mistakes is a Strength

I have no idea why people hold to this belief that admitting mistakes is a sign of weakness. There was Bush's lack of recollection of anything he did wrong (in his defense he probably actually believed it). Now, there's Hillary:

She took full responsibility for the vote, said she would not vote for military
action in Iraq again, and then pivoted quickly to frame Iraq as President Bush’s
war.

I'm no fan of Hillary. I think many people drafted her to run because they thought she could run. I'm tired of that. I want someone who I can get excited about. Someone with the oratory ability of Obama or the surprising outspoken nature Edwards has shown so far. And I'm really tired of political dynasties. We didn't revolt against England only to instill de facto monarchies 200 years later. If Jesus Christ Bush were to run I would have to vote against him on principles.

I just don't get it. The only explanation I can offer is stubborness and a refusal to admit a mistake. I would have more respect if she supported her vote. I would disagree, but I would have more respect.