I truly can't believe that the professor thinks this is a question that could/would/should be answered no and no. I would think this was an object lesson, and I would hope that the professor would warn that she ought to have some tough skin when asking these questions.
So I'm going to ignore the absolute offensiveness of the question and give it a serious answer.
First, not all causes of deafness are hereditary, so any attempt to "breed it out" of the human race would not just be wrong, it would also be futile. There are many posters on this very forum that are deaf because of rubella, scarlet fever, ear infections, injuries etc.etc. So deafness would still exist even if the deaf no longer bred with each. Doesn't that sound just disgusting and humane?
I was not born deaf, and its cause is hereditary. I lost my hearing my right ear first, when I was 20, and realized I couldn't hear out of anymore about 3 weeks after I had gone sky diving which hurt that ear like holy hell. During the free fall it felt like someone stabbed me in the ear with an ice pick, so I attributed the loss to skydiving. I never went to the doctor about it, what would they do? Put a bandaid on it? I had my first child at 23, my second at 25. Right after my second child my hearing in my left ear went from normal to severe in less than a year. This is when I found out that I had otosclerosis. My mother also ended up developing it but not until years after I did. I had no idea this could happen until after I had my children.
There is every chance in the world that my children could develop it, more likely my daughter. I actually do wonder if I had known ahead of time if I would have had children. I certainly would have married, but would I risk my children going deaf later in life? I don't know. I think I would though. Deafness isn't the end of the world, it doesn't make you a pariah. There is a guilt factor there though.
Before I got my hearing aids I was sent all over the place for MRI's and Ctscans, because I was losing so much so fast they thought I might have a tumor. I had to go to Boston to see a specialist, my parents brought me and paid for it since I had no insurance. My mom was just starting to lose hearing at this point I think, and she cried on the way back home, because she knew I got it from her. I think I'll feel the same if either of children end up with it, but I honestly don't know if knowing ahead of time would have affected my decision.
Now, I think this also would be a personal decision, for myself, Not a societal one. I think it's quite obvious that if someone told me that I could not marry or have children because of the likelihood that I could pass this on it would be inherently wrong.