I recently gave a talk where I spoke for 40 minutes in front of about 100 people. Right now, I'm in a period where I stutter on almost every single word (blocks or repetitions). In the end, people loved the talk. I got a lot of positive feedback: some told me my voice was pleasant to listen to, others said the stuttering actually encouraged them to pay more attention. I was also told that there's an adaptation effect : people might be surprised at first, but then they get used to it and stop noticing it after a while. So yes, you can stutter a lot and still speak in public. In fact, it's essential that we are given the space to express ourselves openly. We shouldn't be forced into silent roles just because we speak differently. What your professor is doing is discrimination. He's not giving you the chance even though you want to do it. There's absolutely no excuse for preventing you from presenting with your stutter. It's a very unfair situation.