sorry for off topic, I'll give you fuzzy memories of 1st later as I dont want to take up too much space
He may have been a kyu ranked student from another school who was polite and wore a white belt in your school.
Your instructor may well have known this and expected good control from such a student.
Stopping the fight was probably wise as he showed a lack of control and this person then was asked not to return in private.
This was not on topic to your question of 'what my first sparring session like', just wanted to point out what the Sensei sees is not what the student sees, or does, sometimes recalcitrant students asked to leave show up to spar and the dojo student may see what I can only call 'sanction w/ prejudice' (not understanding the head of school assigned this task )