I agree with you that many things are arbitrary and don’t have to be “girl” or “boy” activities. Such as cooking, medicine, what colors they like, ect...
But I am being truthful that my boys just naturally gravitate to play fighting, guns, ect.
But yes, we don’t want to take that too far. We have this idea that women are better at expressing feelings than boys. In fact my 7 year old son is very outspoken about his feelings, telling us when his scared, or upset, and just tells us that he loves us out of the blue. While my oldest daughter will never admit being upset about something.
You’re as wrong as you can be.