I think he is saying that his parents' are responding with "Who do you want to reach" when prompted with "Who is this?". If you call a home phone and someone responds with "Hello" then it can be quite difficult to guess who you reached.
Also, it's probably more "Hi, this is Mr XXX, who am I talking to?".
Also, it's probably more "Hi, this is Mr XXX, who am I talking to?".