〜たい vs 〜ない for proposing a plan


As I'm learning Japanese with my coworkers in Japan (and they learn English),
I go for lunch everyday with them as agreed. So in the morning when I ask:

> 今日、ランチに行きたい？ (Wanna go for lunch today?)

It is almost a formality since we agreed to go, but just checking whether they
have time and are not too busy. But I've gotten it corrected a couple of times
and told I should say this instead:

> 今日、ランチに行かない？ (Won't we go for lunch today?)

It feel strange asking in a negative way so I'd love some deeper explanation
about it. Unfortunately my coworkers English is even worse than my Japanese,
so I can only blindly follow what they tell me.

So, why would be the latter preferred? I am sure if I understand the basics of
this it'd be a lot easier to remember.

