Lily asked Marshall to do his dishes and he obliged -to avoid a fight. Barney found this ludicrous and explained to Marshall what he would say about the dishes, if he were Lily’s husband.
Fantasy Lily: Sweetie, are you gonna wash that?
Fantasy Barney: I’m glad you bring that up. No. And here’s why – Lily, I know you don’t like a dirty sink, but does that make it my job to keep it clean? I mean, if one day I look up at the living room ceiling and think, “Hey, I’d like a replica of the Sistine Chapel up there,” would it be your job to paint it?
Fantasy Lily: Oh, no! Of course not.
Fantasy Barney: Exactly. So baby, by the same logic, if you don’t like living with a sink full of dishes, shouldn’t it be your job to clean it?
A flawed argument, but I love Barney’s attempt to kick some Id into Marshall :D