So when people study Tai Chi they memorize sequences of movements ( similar to Karate Kata ) but do not learn how to fight to defend themselves

They are told these sequences have secret self defense applications so you can learn how to fight

This is true to some degree but you can learn how to defend yourself much more time efficiently by just being shown techniques and then practicing a modified safe form of them with a partner

However TaiChi has sparring called pushing hands I want to do