Why watch Eva?

[Nuclear Lunchbox]

Reasons why someone should watch Evangelion, eh? It's a fantastic show about human interaction with good writing, great characters, and an intriguing plotline that I'd say is enough to carry anybody through all 26 episodes and the related movies. It stands the test of time pretty well, despite having been released 20 years ago. It's an anime that will make you think to understand it, and will keep you thinking long after you've watched it. I'd understand if he doesn't want to watch Evangelion; it certainly isn't a show for anybody, and I don't think any television show or movie can claim to be such a thing. However, I'd say that Evangelion is an interesting ride all the way through, and at least worth watching the first six episodes of.

You said your friend watches romance shows and complains about animation. I'll repeat the sentiment I think a few others have mentioned: there's not much romance in Evangelion, at least explicitly. You can find romance and draw your own conclusions about the way that characters interact with one another, sure, but it's not a romance anime in the same way something like Tonari no Kaibutsu-kun or Kimi ni Todoke is. As to the animation note, it's good to keep in mind that Evangelion is from 1995-- and despite the fact that old doesn't necessarily mean bad animation, there are definitely episodes and scenes that don't look as fluid (which I'm assuming is the metric that he's judging by) as anime made in more recent dates, still keeping in mind that while old doesn't mean bad, new doesn't mean good.

My pitch is usually just, "Evangelion is a really good show about human interactions, and it has giant cyborgs and cute girls. You should watch the first few episodes with me."

[nostalgic_beer]

Don't show Evangelion to your friend if s/he's likes anime series that have a climax that are understandable at first. The problem with evangelion is that a lot of stuff isn't easily explained in the series.

For example, to know who are the source

SPOILER: Show

of the dummy plugs in EoE Seele Evas

, you have a hint in a 2s second scene:

SPOILER: Show

With all due respect, this is not for the faint of heart. Not everyone is willing to rewatch an anime a bazillion times searching for hints like this and spend lots of time searching on the internet when the series could have explained it better.

Evangelion is a clusterfuck, specially EoE. I perfectly understand those that just hate the series. For the past 15 years that I have shown Eva to someone (from the VHS area), the reactions were from "I can't believe you are so crazy about this anime, it sucks so much I now have some serious doubts about your taste" to "this is the best thing I've watched. But I have some doubts, why the..." and then you explain some stuff, the person gets all excited and start searching for his own and calls you on some unrelated thursday "nostalgic_beer, now I understand why __ happened!".

[Clover]

Recommendations are pointless because people have no taste. They'll do what they want regardless of what you show them, so presenting anything worthwhile is a wasted effort. The only person that matters is yourself. At least, that's the kind of friends I have.
Why watch Eva? That's something that only mattered to you, before you watched it.