How would you react to an E2 who "smart mouths" you in formation?

Depends on the color of their skin. Are they LGBQT? If yes, nothing.
WASP? Discipline to the highest possible sentence.

As has been said at Ft. Benning for "millenia" (it will always be Benning to many of us), the PVT would be pushing Georgia down to Florida.
To be honest though, if the PVT goes so far as to tell you to choose someone else, he/she has been failed by their previous chain of command & I seriously question their drill SGT.
This has to be nipped in the bud quickly! If it happens a second time they would be coming in on a Sat for PT and remedial training.

Dismiss everyone except him and his squad leader. He needs to explain his actions, if he does with respect, accept it. But there still need consequences for his actions. Not only for his understanding but for all that observed the action. If he still has attitude, smoke him!

That would be the last time.

Stand them at attention and explain to them that this is not the civilian world and the they work for the military and they are to obey orders. If not they will be written up. And explain to them what happens to them when they get so many write ups.

Ha! Do the old school thing: Punish everyone else. Explain why they are receiving correcting action. They will make swift correction of his insubordination.

I suggest immediate correction with emphasis on military bearing, being a team member and team cohesion. I further suggest such corrective action be presented at first as an unemotional/unreactive teaching moment for the entire unit. Expressing that the lack of team cohesion is always selfish in motivating reasoning and such behavior eventually will get someone seriously injured or killed. No team can or will trust and/or embrace selfish, self-centered members. If the enlisted person still insists on refusal and insubordinant attitude, I would ask the individual to address the Senior Drill as well as the unit to explain exactly why they are refusing and how they feel their insubordinant manner of behavior is correct. If attitude persists and without a reasonable explanation (i.e. fear or no understand of how to complete task). I suggest the next step would be to issue this enlisted person a direct, legal order to carry out said task. Failure to do so in any fashion other than in a sharp, professional military manner - Article 15, would then be most appropriate.

I retired from Army Infantry in 2003. If this happened to me I would handle this situation immediately and harshly with extreme prejudice. This POS would have become my pet project and would suffer world class Physical Training to the extent that he would be traumatized and regret he ever lost his discipline. I’d do every bit of PT with him FYI. And after the hour’s session of PT, he’d be supervised to complete the original work task he was ordered to do. Discipline and immediate response to orders is what is necessary to complete the mission. RLTW!

This guy clearly joined the wrong branch. Should’ve went Navy!

Assist this errant in transitioning to civilian life.