Are our mothers related? My mother was NEVER wrong! When I was a kid, I just got a slap in the mouth when I questioned her. Later, she just either denied being wrong or "didn't remember." My father, who I adored, used to "invent" people at the grocery store that he just happened to meet and who just happened to discuss whatever point of contention were were having. And they just happened to tell him he was absolutely right. Funny how that happened all the time.
Yes, I admitted when I was wrong with my kids. I raised them to be critical thinkers and to question everything. I also raised them to understand that just being an adult didn't make a person right, so to be true to my teaching, I had to swallow my pride. It wasn't easy, but it was necessary.