"You should not have said that to your teacher."
Translation:To jste vašemu učiteli říkat neměli.
I think the same as a native speaker but not a language teacher.
For VladimirFu8, the answer is here 1.a. http://prirucka.ujc.cas.cz/?id=630
For tbiedl I will try to make some sense of it in English.
The teacher, football players (of our team), famous painters (of our country) are yours, but not entirely. They are also every student's that visits this school, every fan, every art lover's ... It is prefered to use Vaším-naším, over svým-svému.
Where this really matter is the third person. He talks to his children. On mluví se svými dětmi (the kids are his -at least he believes so) vs. On mluví s jeho dětmi. (the kids are his brother's or friend's). But when you say that I love moje děti or své děti, the své should be used but using mé does not change the meaning of the sentence whatsoever and both are fine.