Put yourself in the child's place. Your partner drops you off somewhere and you ask them to stay with you, maybe even run after the car shouting, "wait!" and they drive away saying its for your own good and you'll have lots of fun with the nice people who aren't them?
Personally my kids didn't cry at preschool at least at first because they had secure attachments and it wasn't a problem. My second child did get clingy about 1/2 way through the second year. We simply stayed in the classroom with him until he was secure enough to let us leave. My husband once stayed 45 minutes before our son was okay to stay alone. Yes, he was late to work. Our children our young for such a short time. We choose to make them a priority.
And yes the teacher kept trying to shoo us out telling us it was okay if he cried. We simply stated we weren't okay with that and then ignored any further suggestions.