I think how you feel/reacted is understandable in some ways, but in any case it’s good that you’re thinking about your behaviour and how you can try and be a better friend.
When you said you felt distant from her, maybe she felt worried about where the conversation could end up and didn’t know how to address it properly, because that’s always going to be a difficult subject. Neither of you are in the wrong here; it is better to bring it up than ignore it, but on the other hand most people are going to think the worst, maybe panic a bit and not know how to fix it. You’re entitled to want close, secure feeling friendships, though. Do you feel like people have let you down in the past?