What is the function of the は + ない structure in「初デートで本屋はないだろ」?

Question

Context: https://streamable.com/det3c2

初デートで本屋はないだろ

what is the meaning of this は + ない?

Answer 1

Not sure if you've noticed but there is a similar phrase that occurs in your video clip prior to the line you are asking about.

A: そんなに笑うことないだろ

B: だって、お前初デートで本屋はないだろ

These two lines employ similar grammar structures. 「することはない」means there is no need to do something. See this answer for example. You didn't ask about this construction so I guess you may be familiar with it.

The second one, which you are asking about, is structurally and semantically similar.「～はない」structurally tells us the thing being discussed doesn't usually happen or shouldn't happen. A similar phrase is「それはない」, see デジタル大辞泉（小学館）:

相手の言動を強く非難・否認するときに用いる言葉。それはいけないよ。それはだめだよ。「今日になって行けないなんて、其れはないでしょう」

Also this structure is often followed by 「でしょう」「だろう」. Your line at issue can be rendered as

(Because) nobody goes to a bookstore on a first day.

If you look at the first structure, it shares the same pattern. Although in English there is a difference between "You shouldn't do that" and "You don't need to do that," in Japanese that distinction is more refined and context-dependent. I feel like it behooves this discussion to quote Tsuyoshi Ito's words from that answer:

I wrote “on its face value” because if someone chooses to say that something is unnecessary, it is often because he/she actually thinks that something should not be done. (source)