Mind boggling wrote:
Guys in relationships or married fellas help a brother out!
Because, once she's had a chance to calm down, a couple of hours or a couple of weeks later, and you've forgotten about it completely, she'll suddenly tell you, "No, I'M the one who should be sorry", and you can smile, put your arms around her, and say, "no worries", or whatever the equivalent expression is for you young guys.
Or, if you don't like my answer, or any of the others here, just never say 'I'm sorry" to your lady friend (assuming you have one -- your question raises doubts about that) see what happens, and report back to us.