Well, first of all, that rumour is not true at all. The mechanics of Pokemon don't work like that. I can guarantee you it's not true. Damage of the Pokemon' attacks are affected by the user's attack stat, opponents defence stat, power of the move, multipliers or decreases in stats due to moves (like using Sword's Dance) or abilities, effects of abilities (like sheer force), items and type matchup. These have been the factors since Gen 4, and no mechanics have been changed.
In general, the Trainer's gender means almost nothing. The Pokemon's gender affects moves like Attract and Charm, and pre-gen 6 only males could pass down moves via breeding.
