Unless you discover the man you are dating is actually a woman dressed as a man then you're likely to be dating a "real man".
Having said that each and every person has their own idea of what constitutes being a "real man". Therefore to cut to the chase just say;
"A (real man) is a man who does whatever (you) think a real man does."
Wherever someone lobs the term "real" in front of the words (man) or (woman) it's usually a manipulative ploy to get that person to behave the way (they) want them to behave. They want to shame them.
Instead of attempting to "change" someone you are better off to finding someone who (already is) the kind of person you want to be with. With over 7 Billion people there is someone for everyone!