self depreciating humor doesn't come across very clearly in text form.Ever think maybe I'm using a form of irony when I refer to myself as old and senile, to bring attention to the fact that I know, it's how some of you people see me?
Alternately, self depreciating humor often signals to me that you're okay with being teased about that thing.
When someone is attempting to be friendly they use the terms you have put on the table. If you react this strongly to being 'old' or if it's something that you are this sensitive about it might be wise to not frame yourself as only having worth/deserving ridicule due to age.