We've been teaching our 2.5 year old that hands are not for hitting since he was 18 months old. He was hitting us quiet a bit for what seemed like no reason. Over all he seems to be getting it. I can see that he is starting to understand that it is not okay, and I have seen a huge reduction in hitting. He still gets "rough" when he is overly excited, like with horse play with his father, or when he is not feeling well, but you can tell he's not doing it intentionally. The preschool has not said anything to us about him hitting or pushing other children.
However...he likes to talk about hitting and pushing. I don't know if it's normal. Sometimes he will ask me " Mama can I push you?" or "Mama can I hit you"? We tell him very clearly " no, I don't like that, we don't hit our family or friends". He never hits us after we answer him NO. Today he told me "sometimes I like to push you" and I told him " I don't like that, we never push". Later I caught him singing about how he pushed another kid at school. Is this concerning? Or is this just a normal toddler working through life lessons thing? I have read elsewhere that when toddlers start to learn impulse control you will see them say things like " no hit" before they hit someone. I feel like this is similar to that but I'm not sure and I have nothing else to compare it to because I only have my 1 son and don' have a lot of experience with small children.