Yes, it was a very well respected HS english teacher and I later learned she had many notions that do not fit well with writing fiction. Still bless her soul, she tried to educate me as best as she could... It wasn't her fault.
Just for the record...I do use towards, but only when I am trying to indicate a general direction and not a specific destination.
In my example, which scarlet peaces commented on, the point was he did not move towards the door which is a general direction, he moved to the door which was his destination. IMHO, To would be stronger in this case than towards. Just to clarify...