It seems to me like the interviewer wasn't trying to be rude. I think that he was at first wondering if the stuttering was purely because of stress for the interview and that later he was trying to make you feel more comfortable by telling you that he will do the talking. I myself have light stutter and even i sometimes have a hard time talking to someone else who stutters because i dont know how they will feel if i talk to them about it. Everyone reacts differently ofcourse and it is hard to judge how someone will react to what you're saying. Anyway, I hope you get the job and later on in life learn that stuttering isn't all that bad (I myself am still not there, but i feel like i'm coming close). Goodluck!