The literal answer to your question would be Rule Zero: if your DM says you can't, you can't. Your DM can make any house rule he wants.
But the more sophisticated answer would invoke Rule Minus One: If your DM is a stupid male chauvinist [expletive deleted for the benefit of Eric's grandmother], you don't have to play in his campaign.
Tell your DM what a jerk he his. Tell him I said so. But don't tell him where I live, because he could probably beat me up if he wanted. Most people can. Including most girls. If I were a D&D character, I'd have STR of about 6. You know, that's never stopped me from playing a fighter. My very first D&D character was a human fighter named Orsal. I chose my ENworld screen name in his honour, even though he had STR 6 and INT 16, and I probably have STR 16 and INT 6. My personal weakness never stopped me from playing a fighter because -- and here's the point that I thought would be obvious enough, although your DM doesn't seem to grasp it -- the player is not the character! When my fighter character swings his greatsword (we called them 2-handed swords back in the day), I the player sitting at the table don't have to lift anything heavier than a 20-sided die. And even with my STR of 6, that's not too much of a challenge for me.
I suspect that your DM really doesn't want you playing. He'd rather have an all-boys club. But he doesn't want to be too explicit about it, because he's hoping people won't notice what a sexist [expletive deleted] he is. So he's just going to come up with difficult house rules just to make life difficult for you, hoping that you'll quit on your own volition.
You could stay just to spite him. But you wouldn't enjoy that. If he doesn't want you in his game, you're not going to enjoy it either, and it would be a shame to spoil a great hobby for you just so that you can annoy a jerk of a DM. So here's what you should do instead. Find yourself another DM who isn't such a [expletive deleted]. Join his or her campaign, create your paladin character, and have as much fun as you can playing. Get into character really well, and make things a lot of fun for everyone around you. Then have your nice DM call up your nasty ex-DM and say something like "You know if you hadn't been such an obnoxious jerk one of our best players would never have joined us. I just wanted to thank you for your idiocy."
By the way, if your DM decided female characters couldn't be paladins, because the society he was creating wasn't openminded enough about gender roles, that would be a totally valid use of Rule Zero. But as long as there are paladins in the campaign world, and they're appropriate for a PC class, there's no valid reason to restrict certain players from playing them on account of their real-world sex. If a wimp (and a pacifist) like myself can play a character who kills ogres for a living, real-world player attributes should in no way restrict in-game character attributes.