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These usually evoke a good laugh from the girl, but I wonder if it somehow subconsciously draws their attention to my flaws and turns them off.
I think it is turning them off. You are the king of your castle, act like it. I self-deprecate all the time. I'll admit something about myself and tell the girl "i bet you're glad you're with me now huh" or whatever, just making myself out to be a human. The girl likes these admissions more often than not.
You have to feel confident in yourself first, then the deprecation is showing that you aren't some perfect person after all, which the girl can relate to. In your instance, you are insecure about some issues (which you shouldn't be) and then you're trying to deflect that.
It's a fine line. The key is in feeling you are a highly valuable human being first.
If you are deprecating something that may be a more obvious "flaw" (in quotes, because what you are speaking of are not flaws) then IMO it may likely be in fact showing an insecurity to the girl as you are suspecting. On the other hand, if you were to state a story that happened to you like you fucked up so hard on a final because you went to Vegas and were on a bender even though you're usually responsible, this is called admitting you're human.
WHEREAS, most guys are only showing their good side and it is a huge interrupt when you are able to show the girl - I am human too - we all are - we all fuck up from time to time - we all have our flaws ........... when you can do this, you are severely separating yourself from most other guys and putting yourself in a good position.
IMO the key is not to make the flaw you introduce something that the girl will readily see or suspect may be a weakness for you in your mind.