I think it's quite hard. From the examples that Sanjeev gave, well, they might seem trivial but isn't that the point? That it's not only big issues like the prevalence of domestic violence or horrendous things occurring in other countries or pay gaps etc but it's the everyday stuff, the drip-drip effect, if you like, which is just so constant and depressing.
Take the trousers, for example. Would it be funny if the original meme said "Give it to your Chinese mate. That's what they're there for!" Of course it wouldn't and no company would dare print that on their trousers. But women are fair game.
I think that with DP he doesn't think that sexism is a problem because it's not immediately obvious, and it doesn't impact on him. He once described me as a "massive feminist" which I really am not 
I think of myself more as a teeny tiny babysteps feminist. He will describe some horrible sexist thing one of his work mates has said and then say "But he's an alright bloke apart from that." I disagree! How can someone be "an alright bloke" if they are sexist? A character trait like that impinges on everything that someone does or thinks.
The thing I try to remember when I am talking to him is what I was like a few years ago when I didn't know anything about feminism. I would have probably poo-poohed various things as nonsense or overreacting too, it's only with the benefit of having read and absorbed lots and really listened and thought and digested stuff that I have understood why certain things are problematic. You can't make that kind of deep understanding happen in a single conversation, you can only plant seeds for further research/reading/exploration. Ultimately it's up to them whether they believe it's a valid cause or not.
I have found that when talking to my mum it's a lot easier, she doesn't identify as a feminist and seems to think that some of the things I say are extreme but with certain things, like for example if you are having a conversation (as a woman) and you get slightly annoyed or passionate about something, it can quite often be taken a totally different way to a man talking in the same tone about something. She gets that, because she's experienced it, whereas DP hasn't because he is male. Similarly, talking about porn and why it's threatening and aggressive, she just gets it, whereas DP doesn't. It's because it's really hard to step into another person's shoes and imagine a situation from their point of view. Especially when that point of view is almost never present in the media, etc. Probably the reason women supposedly find it easier to empathise is that we are always being shown the male point of view, the male opinion, it's easy to empathise when everything you interact with, media, pop culture, professionally etc comes from the male point of view.
Did you know for example that they only ever show men on TV having heart attacks? (Mainly because you need to use a defibrillator topless.) And that the symptoms for women are in fact different (more likely to have pain in the jaw and/or back rather than the chest and/or left arm) - but very few people know this, because it's always men, on TV, having heart attacks. Again, it's a trivial example, but quite shocking, if you think about the potential consequences. And probably one you've never even thought about.