After reading through the thread, I'm piecing together ideas other people mentioned along with my own thoughts on the matter. (Sorry about the length)
From Dora's POV:
Boyfriends are all assholes, at one point or another. And being an asshole means hurting her specifically, possibly physically but definitely emotionally through some sort of trust-breaking action. In other words, she was too trusting in the past and got her heart and emotions totally trampled on. It doesn't help that she sees her older brother treating women in a similar manner to which she was treated. So she tried to toughen up.
And now she's dating Marten, a guy who, as far as any of us know, is the nicest, most willing guy ever. And that whole concept is foreign to her. No guy is ever like that, even if he starts out seeming like that. And the longer she dates Marten, and the longer he continues to be awesome to her, the more paranoid she gets about the whole thing. So every little thing that could possibly, in any way, be construed as Marten being the asshole she (subconsciously) expects him to turn out to be, she blows way out of proportion. It's supposed to be the Thing She Loses Trust over, but then Marten turns around and doesn't act like the other boyfriends again - he talks it over, lets her express her doubts, and they move on. But Dora can't quite shake lose this lack of trust.
And then they're talking about porn. Dora is curious about Marten's - she's never even seen him watching any. And then Marten doesn't want to tell her about it. Alarm bells go off for Dora - this is it, this is the Thing. Not only does he express a desire to not share any details, he tries to a "tough guy" defense. And Dora thinks that yes, she's gotta know what's going on here because finally, what she was expecting all along will happen. (I also think that Dora's got some kind of a complex about always being right, but in this case it's more subconscious.) So Dora goes to ask Pintsize, figuring Marten will have him take care of it (showing, in some aspect, that she doesn't know Marten all that super well anyway), and Pintsize doesn't know, but he does know it's on the laptop and he'll show it to her (they just gotta figure out the password, maybe). And Dora finds that the porn is nothing at all - just regular run of the mill stuff. Again, not the behavior she was expecting.
Again, Marten proves to not be the guy she thinks all guys are gonna end up being. And then he's all up in her face about it, and she can't figure out why. If it were one of the other assholes, he'd be mad because she just found out some secret about him, but it's not really the case with Marten. She crossed a line with Marten and didn't even look back, and now she doesn't understand because Marten is not what she's expecting him to be in the slightest.
Marten's POV:
Surely growing up with a mom doing what she does can sometimes lead to awkward conversations for him. It can't be fun to be hanging out with some guys, and the conversation turns to porn, and he hears about them jerking off to his mom. And then they ask him if he's watched Veronica Vance, and when he says no, and they get all on his case about why not, she's so hot and whatever, to have to tell them she's his mom...it's probably just not so cool. Suddenly they can't look him in the eye anymore, and the whole night turns weird. So he's probably learned to just not talk about it. Not really. Or rather, not specifics. If he lets 'em think he's into something so kinky and odd that he can't even talk about it, all the better. Beats having to hear about what they think/do concerning his mom.
So Marten just doesn't talk about it. And he most likely feels like it's private anyway - why wouldn't he feel private about it, especially when his mom isn't particularly. And maybe that doesn't mean he won't share it with his SO eventually, but it's probably gotta be on his own terms. He needs to feel safe about it...he needs to trust the person. And I can see him not being too comfortable sharing that with Dora right now. Especially after they just had a big trust argument. (and he already knows Dora is a fan of his mom and watched her as a teenager...I can see him not particularly wanting to find out she still watches her.) Besides, he doesn't particularly wanna talk about it in front of Faye.
So when Dora pushes it (and he's not surprised she did, she's way more chill with discussing stuff like this in the ear-range of anyone), and he tells her it's private and he certainly doesn't want to talk about it here, and he'd like her to not really go into it, he's actually a little surprised that she leaves, saying she's gonna find out. And then he sees her on his computer! Talk about a violation of trust. Marten has no doubts, I'm sure, that if he was looking up things about Dora on her computer she'd throw the most Epic Rage Fit ever, and so he's totally baffled as to why she doesn't see her actions as a gross betrayal of trust.
In other words, these two continue to have the worst communication ever, and to be a solid couple, they are going to have to really work on that. And Dora really needs to go into therapy. Marten maybe. Dora needs to learn that just because she's cool with sharing whatever, doesn't necessarily mean that everyone else is - and just because they aren't doesn't mean they're hiding something.