Though the did-I-offend-you question is mildly irritating, the comment about being shy is moreso.
I agree. My take on reading this is that the neighbor is (possibly consciously, or possibly because it's worked for him in the past) using a tactic to put OP on the defensive.
I feel like he's trying to put her in a position where she'll overcompensate and then he'll get the response that he wants which is more of her attention and her time.
If OP is the type to be meek and a people-pleaser (which I don't believe by this post, but maybe what he looks for in a friend and/or girlfriend) she would react by:
-going out of her way to be overly nice to prove to him that she was not offended and
-going out of her way to talk more to prove that she's not shy
It's kind of like he's prodding her to disprove his statements or justify her behavior somehow.
That's my take on it. I feel that it's manipulative. If he were less pushy about things, I might have a better feeling about him. Knocking on her door, initiating an action in order to "accuse" (perhaps "intimate" is the verb I'm looking for, "accuse" sounds harsher than I intend) her of being too shy just seems pushier than necessary.