There's a certain Americanism to the whole gun dialogue. I'm not even sure why the option to have an opinion about being given a gun was there, it's very obvious it's related to american gun culture and the discussion surrounding it (to even mention New York laws there lol) but did the game really have to take it there?
I wouldn't really bat an eye to a gun (or not being given a gun) but the whole dialogue option thing there did stand out. I just wouldn't have noticed or cared otherwise.
The only thing lacking is Laura screaming about the second amendment or something.
I'm sorry to inform you that the game takes place in America... Specifically New York... Where New York's laws are in place... So it's relevant information.
As for why the conversation option was there. I can't tell you what it will later effect but that was an archetype choice.
Noble/Heroic Null doesn't want to resort to using a gun because killing is against his morals.
Conflicted/Practical Null understands that a gun is good for self defense.
Bitter/Anti-Hero Null is just done ending up in the infirmary and willing to put super villains in the ground or at least make people hesitate once they see he's packing.
Edit: Laura doesn't use or need guns. Girl can outright dodge bullets in some cases. The only character I can think who'd scream about the second amendment would be Deadpool but in an ironic way since he's Canadian and probably doesn't even know what the American Constitution or Bill of Rights says let alone care about it.