Generalizing doesn't include exceptions to the rule. There are always exceptions to the rule when it comes to human behavior (thankfully). However, it's also important to note that from what I've seen in the last few years on social media and "debates", exceptions are often touted as a reason for completely discounting and invalidating generalizations, which is not only ridiculous, it can also be dangerous.
Here's a loose example to illustrate:
Generally, long term tobacco usage is detrimental to the health of people who smoke. That's a fact. MOST people sustain deleterious health effects from the behavior. Is that generalization stating that ALL people will experience deleterious effects from smoking? No. There are some exceptions that occur (very few). Imagine someone arguing that because there are some exceptions to that rule, the generalization isn't valid and shouldn't be proper.
It could be said that generalizing is a necessary, important and valid means of calculating, quantifying, identifying, analyzing and reacting to threats to people as a whole and therefore to our species. The error is both in not acknowledging the exceptions and discounting the validity of the generalizations because the exceptions exist.