If you accidentally hit someone with a frisbee, you apologize. In this case intent doesn’t matter because the context makes it clear you’re apologizing for an accident.

However...

However, if you’re in the middle of a two-sided debate and someone demands you apologize for hurting their feelings, and their feelings were hurt based on a misunderstanding or mischaracterization, this is not the same situation.

The context does not make it clear you’re just apologizing for an accident. The context makes it seem like you’d be apologizing for your opinion itself, and validating the misunderstanding or mischaracterization.

This is an emotionally manipulative tactic. If your kids pull it on you you should shut it down. If you pull it on someone else as an adult, you probably need to get a better handle on emotional reasoning.