If we apologize for our bad behavior only if others apologize for their bad behavior first, we are being childish and irresponsible. We are part of the problem. Best that we apologize when we've done something wrong, regardless of whether or not people apologize for what they have done that is wrong. This is taking ownership and responsibility. This is taking the high ground. This is being an adult. This is strength, not weakness. This is the right thing to do, particularly if you want to solve problems rather than perpetuate resentments and misunderstandings.