No, its not against the law for a 20 year old to DATE a 16 year old. The definition of date means to go out together to a movie or to dinner or dance. It does not mean having sex regular or oral.

Is it illegal to date a 16 year old when you are 21?

Generally, it is not illegal for these two to date. Of course, any sexual activity is considered statutory rape, but if there is no sexual aspect to their relationship, then they are probably fine. However, this is a fine line to walk for the 21 year old.