There are two reasons for saying it. It is a way of saying "Why did you bring the subject up?" "How do you like your new car. Is it good to drive?" "Why do you ask me? Are you thinking of getting one yourself?" There is nothing wrong with this meaning. This is the meaning it has here, I think. It is also a way of saying "I am surprised you asked because I don't know anything about it." It would be better said, "Sorry, I am not involved in what you asking about, so I can't give you an answer." OR "Sorry, but this is not my area, so I can't give you an answer." I don't like "Why are you asking me?" It is somewhat impolite and makes the person who asks feel awkward.

A. Thank you for coming. B. Why did you ask me? A. We need you. And you're one of the few people I trust. B. And you still trust me, now that we're... The second sentence means "Why did you ask me to come?". When A thanks B for coming, B asks why A asked B to come. A then replies that they needed B since B is one of the few people A (and team) trusts.

The person says "Why did you ask me?" does not know why it was he/she and not some else, who was asked to come to the meeting. Other way of saing the same thing would be, for example "Why did you ask me to come here?" or "Why did you ask me and not some one else?"