Gen -- your mom is so cool! You're right -- that guy was a jerk! Fortunately, not all trainers are that way. The BEST thing that ever happened to me was finding a trainer who taught me how to work out "like a guy" ( I was told that once like it was an insult -- I took it as the highest of compliments

). He put me through the same workouts that he did -- none of the "high reps, low weights, machines only" stuff that some trainers stick their women clients with. He promised me that if I lifted as heavy as I possibly could, I'd only get smaller -- and he was right.
So your instincts were absolutely correct -- there aren't "male" and "female" ways to work out. It's all the same and you're right to demand that your workouts not be "dumbed down" just because you're a woman.