I've often thought (though certainly never said it in real life) that younger women who shirk the idea of frminism often lack a certain amount of empathy and also a seeming inability to see the bigger picture.
Empathy - because they've never experienced sexism themselves, and see their opportunities as the same a their male peers. Indeed, I am 37 and have never really experienced sexism, but I can see the bigger picture - that it's not all about middle-class white/Western girls from happy, supportive families, who've gone to university, got well-paying jobs and have nothing but lovely men in their lives.
If you're only 18 and haven't yet gone out into the world, then it's hardly surprising that you'd come to the conclusion that feminism is outmoded.
But, if you take those blinkers off and scratch below the surface it's difficult (impossible, I'd say, but a foray round these boards proves otherwise) to ignore the continuing inequalities between the genders.
I have to say I'll be gutted if my DD doesn't align herself with feminism, I'm not going to lie! Yes, of course, she need to form her own opinions, but hmm, I won't go into why I would judge her since there are zillions of readers and lurkers ready to jump on my reason. 
I agree with the others who say try not to get too het uo when discussing his with her, and try to tease out her arguments so that she can come to the right her own conclusions.