As a man, he is expected to always apologize for any mistake. However, I don’t believe this should always happen. The wife will never be held accountable.
Instead, apologies should always be made when something has been done wrong. When discussing the issue, ugly things may have been said. That is when apologies should be made. Otherwise, both sides should compromise or come to an agreement about the issue at hand.
The man should not always feel obligated to be the first to apologize to his wife or girlfriend. Both sides should apologize if they are truly sorry for what they said or did. Plus, both sides should figure out how to resolve the issue before moving on and putting the past aside.