For me it is disrespectful to interrupt someone speaking, so that is why I find it "weird". But it is most probably a matter of preference. I don't think everyone should have discussions on my terms.

In the context of interviewer<-->interviewee, though, I think it is generally more interesting to listen to the interviewee than the interviewer. It seems to me that the whole premise of the interviewer<-->interviewee is for the interviewer to get the interviewee to talk.