I didn't realize that the habit of starting sentences with, "Sorry, but could you..." actually made me present my own needs as weaknesses. It was probably clear to the other person, but the reason it wasn't clear to me was because the word "sorry" had subconsciously made me feel as if I was constantly bothering other people.
Many people say that having your children say "I'm sorry" when they aren't really sorry is invalidating. I am certainly against invalidating your kids, and I do not recommend telling your kids that they ARE sorry when they aren't. However, I do think that children should be encouraged to apologize if they hurt someone physically or emotionally, and here is why.
I have noticed how often I -- and my female friends -- apologize for things that are out of our control. This, of course, is different than saying, "I am sorry for being late," or "I'm sorry I picked a fight last night because I was really hungry and you were taking forever to figure out our plans."