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.

Talk with your senior chief and assign all the shittiest, most fucked up details this little shitbird. You’ll need backing so that this doesn’t look like you are just picking on this guy.

Have him clean holding tanks and shitters and anything else that no one wants to do.

You can break him of this.

Make an example of the soldier in front of everyone. Two soldiers hate to loose, time and money.

In the former Army of the 60's and beyond, I would have taken him to the back of a building and kicked his ass. That usually worked. If it didn't work he would be given an Article 15.

Immediately pull the soldier out of the formation (having the soldier stand by by while getting the rest of to work) Then issue a counseling statement, getting the Platoon Sgt involved if needed. This would be a ONE TIME ONLY warning. They do it again and I am going to put them in for an Article 15. I have done this a few times. (Usually it only takes one wake up call to get the soldier to wake up and smell the coffee). Most times between me and the Plt Sgt we were able to take care of things.
Every time we brought a soldier up for an Article 15 for this type of infraction, the commander would send it up the line for a field grade Article 15, if for no other reason than to send a message.

I am not talking about the usual moaning and groaning and bitching and whining. I am talking about the egregious stuff. In the Army everybody bitches and whines

To put it bluntly, in Grunt terms, if their TL and SL didn’t immediately jump in that kid’s 4th point of contact, there’s a bigger problem in that unit. Crush it, with an appropriate punishment, like CQ, SD, and any extra duty that comes up for the next month. Reason #439 why I got out; in my day I would smoke them until I got tired

Counseling statement as your order is lawful. If the assignment was given, the E2 should do it end of discussion. Im a fresh E5 and I've had my share of times were I didn't want to do an assignment, but I knew how my NCOs would respond if I hadn't.

Do a reverse psychology on that insubordiante individual, and reverse the roles , (only after dismissing the remainder of the troops), but keep his platoon leader with you so both will not say you are picking on that individual, and or she will go above your head and report you of abuse or mistreatment. Do exactly what he did to you, and the same to him and then ask him how he licked it. When, and if the individual did not show remorse or apologize what he did wrong, then say to him and the patron leader that if he disobey orders or if he acts continuously in this behavior, then you have report his actions in give him article 1 USMJ. If he continues to be a loud mouth and disobedient then reduce whatever rank they hold . The patron leader E-5 would need to have a talk to as well, not so much in reprimanded but to get this individual in the right path. Will this work, possibilities it might work, and then you can go about your everyday duties, if not, then removal of the arm forces.

He would be cleaning grease pits for the next month!

I am old school... knock his ass out.

Take their time. Physical punishment isnt gonna solve squat. They do PT every morning anyways so that’s free. Have them write an 5 paragraph essay on the importance of following orders and the consequences of insubordination, give them a due date and start a paper trail. This not only teaches military style writing early on but helps with his mindset. His refusal to follow orders is a mindset. True leadership is inspiring the solider to change his mind on to why he should follow you not because you have stripes on your chest. That’s call ego and no one follows ego. Once YOU change your mindset that you aren’t the best thing since sliced bread because you have stripes and start leading by inspiration that’s when this won’t become a problem. Yours truly, the E4 Mafia.