Hello this is Shiho from Japan.
Man-date means friendship meeting among two or more straight men. I can see a male date is so difficult thing from this short sequence because Peter always failed to make good relationship with other guys. However, I think a male-date is not so hard in real life because I think that getting formal dinner is not only a male-date but also just chatting with other guys can be considered a male-date. I can say Peter is just unlucky guy.