I'm second-guessing my future career too. I'm pursuing a degree in English and in my country (Italy) most of graduates from this programme end up being teachers... Given that, one day I might be a teacher too. Can a person who stutter teach well English to their student? We're in the same boat, but keep in mind that a teacher is often described as good teacher for their empathy and their attention to the students. A teacher can be extremely good at communicating, but they may be lacking a more empathetic and human side. Of course, it's up to you to decide whether you want to be in that role or not. There are also ways to improve with your stammer if you feel like to be a good teacher you need to overcome this "problem". I send you a hug, I feel you