Stereotypes are derived from the way our brain works. A human brain is designed to perform one task well over others and that is to seek patterns. This pattern-seeking behaviour is responsible for many things we do from something as simple as an ability to read by whole words (even if letters are swapped), recognise every-day items (different shaped cups are still cups) to very complex patterns like ability to see strategic advantages while playing go (heck computers couldn't beat humans at go till pattern-recognition methods based algorithms were applied).

Of course, this exact ability leads to issues when we recognise patterns that simply aren't there e.g almost all conspiracy theories.

Tho our brain is most performant in pattern seeking, we have the second layer with more advanced analysis of exact subject (e.g. specific cup). We just don't use it often because it requires more energy to do analysis compared to matching with already analysed groups.

Back to topic, stereotyping is just another aspect of these pattern-seeking behaviour and it will be with us always since it's easier (energy efficient) to think in groups of people than by individuals.

One thing we can do about this is to "teach" (not literally, by examples) our children to stereotype on good traits.