To be fair, this is not a lie. The teachers were unknowingly giving you a Type-Theoretic answer. The answer to your questions change dependent on the Number Type you are calculating with. :)
To be sure, there is a habit to make the teacher's life easier by lying, and I certainly believe you when you say that you were lied to; but all of these can be rescued, as a sequence of decreasingly incomplete truths, just by adding quantifiers. Since the human brain is (excessively) good at ignoring quantifiers, a skilled teacher (not me, in this context—I'm a college teacher, so am not claiming that this is the right language for primary schoolers, just that it's true) can speak truthfully without impairing the pedagogy:
Q. how much is 3 - 5?
A. taking 5 out of 3 does not give a whole-number answer.
Q. how much is 2 divided by 3?
A. dividing 2 by 3 does not give an integer answer.
Q. what are the roots of the quadratic function ...?
A. this quadratic function doesn't have real roots because you can't take a real square root of a negative number
Q. how much is 3 - 5?
A. nothing because you cannot take 5 out of 3.
Q. how much is 2 divided by 3?
A. nothing because you cannot divide 2 by 3.
Q. what are the roots of the quadratic function ...?
A. this quadratic function doesn't have roots because you can't take the square root of a negative number
I believe it's possible to not lie when teaching math, but I guess it's harder to do.