Dan seems like a guy that won't like anime no matter what you show him, and will use any anime he deems bad as an excuse to continue hating anime in general, despite the, what, two? Three? Four anime he tried? And the fact that you keep giving in to his hatred rather than try to argue against it, for the people watching who are avid anime fans, makes arguments like these feel very bias. I may be wrong, but that's how it's coming across.
Maybe try getting someone on your show who is big into anime to help counter his arguments. I remember a while ago you guys did a debate about Anime vs. Western animation, but both debaters were people who only seen a handful of shows. It didn't seem like a fair argument when one guy is bashing anime and the other guy's simply like "Yeah... you got a point...." I'm not angry or offended, it's just rather depressing having to hear anime discussions from one person who hates anime and another person who's only mildly interested.
My anime suggestions? Well, my two favorite anime are FLCL and Puella Magi Madoka Magica. I see you enjoyed FLCL, but Madoka would probably rub you guys the wrong way. It's a magical girl show, in the same vein as Sailor Moon, but a much darker take on it. It's on Netflix and it's a very popular anime. But again, it might be a show that both of you will take issue with. So no, I got nothing. For Dan, I don't think there is an anime that would win him over. There might be an anime he'll like, but nothing that will convince him that there's more to anime than DBZ or Fullmetal Alchemist. I, like most anime fans my age, got into anime very young. If he never got into it before then at his age he's far too jaded and cynical to be open with it.
As for Attack on Titan, I still enjoy the series. Not one of my favorites, but it's a fun ride, and for me that's all it really needed to be. Honestly I like the second half better than the first.
Also, I've seen some truly, truly terrible anime, so if you think Attack on Titan is terrible, then lets just say you came off easy.