When a girl asks what is the worst things you've ever done what is a good response without giving it away?
The purpose of talking about yourself is to show brief insights of excitement and intrigue. Never reveal all your secrets; always leave room for possibility. In this circumstance, it seems to me that she wants to test you for vulnerability or weakness. If you paint yourself as this perfect man, people know something is peculiar.
In this situation, you actually end up being a weaker man by failing to end on a good note. You leave her frustrated with you because you won't admit to having flaws. She needed confirmation of a realness and vulnerability, and that failed to appear. Instead, you covered up your flaws, and hid them from her. No layers peeled off, you created a standstill in intrigue. If you can't tell her at least a little about you so that she hooks onto your story, her interests will start to decay.
Luckily, vulnerability has been talked about quite often on GC. In order to build intrigue, do not release the entire story right away. Saying the worst thing you've ever done was accidentally hurting someone you loved instead of saying you cheated on your girlfriend, and leave it at that. Give her a little bait, and she'll stay hooked onto the story, and you can slowly reveal facts of the story without actually telling her how it unfolded. Mind you, don't reveal all those facts in one conversation! Just start to do it gradually throughout getting to know her if she probes you about it the following weeks.
Intrigue comes with being unexpected; do NOT reveal anything that seems likely. If you seem like a nice guy, revealing that you hurt someone you loved will provide more intrigue than saying you accidentally killed a deer and felt bad about it. Similarly, if she thinks your a bad boy, saying you accidentally hurt someone you loved will prove bad. It's expected. Revealing that getting away from abusive friends helped you when you act like a bad boy, and they feel like they are uncovering something new and unexpected.
Remember to keep it quick and sweet. Talking about yourself will NOT build her connection with you any closer. You'll feel more connected to her, sure, but her connection is based off of how comfortable she is with you, and how much she talks to herself about you. Talking about yourself is for showing that you are an attractive man by providing vulnerability and intrigue; it does nothing to form a connection whatsoever. Provide insight and intrigue into your exciting life that has existing vulnerabilities, and you'll find things with women will become smoother.