Could you teach me how "go out" became to mean "date someone"?
You can understand "go out" as being short for "go out on a date," which is related to the concept of dating. Thus, to "go out with someone" is commonly understood to mean "date someone" or "go out on a date with someone." Ex: I went out on a date last weekend, but it wasn't very fun. Ex: I went out with Peter during high school.