I'm not a person who stutters, but an SLP. In grad school, one of our professors brought our attention to how stuttering has historically been used to portray nervousness, idiocy, or villainy. Since then, it's been one of my biggest pet peeves in media. I think, in Quirrell's case, it's an especially bad look as the Harry Potter series teaches its readers to overlook assumptions about others. So the usage of stuttering to make people believe "oh this guy is so nervous that he can't possibly be a threat" is bullshit.