All generalizations are not true- that's a paradox, that in itself is a generalization.
What about this one: "all people are equal in rights and duties", or at least they should be? Shouldn't that generalization be true? Should all people be treated equally when it comes to law?
But we can definitely say that most generalizations are not true. Like: "Nobody understands anything", "I know everything in the world", "all women lie", " all redheads are evil", "all people are the same" (no we're not the same), "all men are unfaithful".
Most of the time when you generalize you become unfair to someone. That is when all the labeling problems start. So whenever you find yourself generalizing, think again. That is of course you care about not doing wrong to anyone.