The thrust of what you say seems to be that she is unreasonable. That's not how apologies work. Is there a history of her expecting you to be "perfect?"

Whenever someone couches an spology in the context of "I'm not perfect." or "I'm only human." or "I made a mistake." that pretty much negates the apology.

Whatever you said came across as you finding her unattractive. I don't think I could stay with a guy who I believed did not find me beautiful. It sounds to a woman like the guy is saying, "I'm with you because I couldn't get a really pretty girl. So I'm willing to settle for you." A woman thinks, "Hey, don't bother."

That she still wants you as a friend sounds like she's leaving the door open and might even be hoping that you will win her back. Being real sorry - and I believe you are - doesn't matter because she believes what you said is how you really feel. That's what you have to undo. Since you want her back, you must feel some attraction to her. That's the message you have to play up.