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

Had that halo to me....his/her time off was spent doing many “interesting duties” such as sweeping the whole unit building, writing reports for other subordinates a d having them checked by said subordinates; daily duties such as this while other subordinates were off duty those souls learned not to mouth off! IE...your time can become my time with a bad attitude

In my 40 years in the military, I have never seen anything like that happen. If it had, it wouldn't have happen a second time. It sounds like someone has taken their relation ship to an unhealthy level. In the military, at all levels, you have leaders and followers. You need to know what your role is at all times. It sounds like that soldier was not indoctrened right to the military way of life. That E-5 needs to take that E-2 off to the side, away from the rest of the soldiers and counsel that soldier. It needs to be put in writing and kept at the E-5's level. Unless, the same thing happens again, then he needs to get his Squad Leader involved.

When acting in my normal MOS duties I never had a problem but it was a technical MOS which required a higher GT score. But while in Detail Branch at a training post where I ran a grass cutting team and later as what I called "The Post Commanders Head Gardner" taking care of the grounds around 3 Generals & 3 Colonels quarters using detail personnel from training companies, I would occasionally get someone who wanted to goof off. For those I had special jobs for them to do. Especially at the Post Commander's quarters where my favorite job for them would be to hand them a rag and a can of Brasso and introduce them to the brass cannon in from of the General's quarters. I expected them to work hard while there but treated them fairly & not cuss them out and would give them good breaks when they did work hard. After a couple of months of this, we noticed at the Detail Branch office where I picked them up, that they would jockey around in the formation to get in a spot where they would end up with me. Those who were frequent flyers knew that they were doled out to the teams in the same order. Had a female soldier use the excuse of being on the rag. That being the 1st time I had heard that excuse I let her do a little less. That night I asked my wife & oldest daughter and that was the last one to get by me with that excuse.

What you have here is a soldier who hasn't learned respect for the "Service", his unit and comrades, those who are in charge and no respect for himself. As the NCOIC you have the opportunity to mold a good soldier or piss off an angry one and lose a good soldier. To me it would be time for the kid gloves and in a very low voice I would kindly ask the PFC to see me after formation and go about my business of getting the platoon started for the day. You have squad leaders to see that the work gets done so you can spend some time with the errant PFC.
I'd then take him to the mess hall, get some coffee and wangle a snack out of the cook and have a seat where there are no people nearby. This kid has a problem and thinks nobody cares. You need to find out what the problem is and see if you can help. Could be some little thing in his platoon or something big back home that the kid has no control over. Help if you can but by no means do you berate the kid nor give him hell and any punishment at this point. You already have his attention by being nice to him so make use of that and send him back to his squad or unit with the reminder that he is a soldier first last and always and he needs to conduct himself in a respectful manner at all times. I'd keep tabs on the kid through his squad leader and my own observations with brief chats on occasion and encourage the soldier to keep at it and do the right thing. The PFC pushed you to the wall and you gave him a break. He didn't expect that and now owe's you something in return and he knows it. If you get the favor repaid that's great. If not there are many ways of handling a recalcitrant trooper. I'd try the nice way first and the worst way last if he didn't improve after that. Hell, it worked on me so why not him? Been there done that.

Tell them to bring a battle buddy and see me after the formation. They and their buddy will do the task and the pvt will get a counseling reflecting his or her behavior.

End it right there. Keep the formation as is and Pvt Ass Wipe gets an ass chewing and an explanation of the importance of carrying out all lawful orders given by those above him. Pvt. Ass Wipe gets an Article 15 with a recommendation that his military service be terminated after a few months in the stockade.

PT his ass until he drops! Then give him an Article 15, reduction to E1, extra duty, and restriction to post for 30 days! You have to show him and everyone else that this behavior is NOT acceptable and that there are consequences!

PT his ass until he drops then give him an Article 15, reduction in rank to E-1, restriction to post for 30 days, and extra duty! Make an example of him so everyone else will know that this isn't a game!

LTJG (Join to see) Well, I realize the photo doesn't necessarily correspond, but I can't help including it in my response:
Step 1: take those PT belts off
Step 2: have troops dig a big hole
Step 3: throw PT belts into hole
Step 4: fill hole
Step 5: smoke the E-2 like a cheap cigar

As an Ex NCO (AJ E-4 - for clarity) - I would pull the wise ass Pvt and his / her team squad lead to an office / separate place and set him / her straight - orders are orders and thats it... nip it in the bud....complaints come later...compliance is paramount right now.... As a Commissioned Officer ( which I was later in life) - I would simply monitor what the NCO did and intervene only if need be and then (maybe) whisper into the Pvts ear after the NCO was done that he had better take the advise of the NCO and move out....

Violence is not the way... this coming from the main question and the comments. Back in the 1900 people people probably didn't fight back or he was out numbered but I guarantee that made him no better of a person/leader than kicking him out would have words are extremely powerful maybe slick sleeve lashed out on bad leadership/hazing. True he picked the wrong way to go about it. Wall to wall counseling or woodline institutionalizations don't respect the person either

I had a situation as an E6 where an E4 did this. I assigned the work to someone else then asked him what was going on. He told me I wasn't his boss and to f$co myself
Yes minutes later I get "invited" to see the CO.
Yep did that E4 is claiming racial discrimination. I get asked how I determined who to put on the detail. I told them I looked for the first 4 people I out ranked. The other three were not the same race as E4 did that. CO art 15d him.

Find out in private wtf? If it is attitude help him understand what he just chose for himself

As an O5, my first thought is that I'd turn him into an E-none. I appreciate that he might be undergoing some issue that caused him to snap, but it doesn't excuse his actions and must be corrected on the spot.

Ask them if they would like to tell that to the CO. They enlisted not forced as some were back in my day. When I joined all Marines were volunteers so that meant you did every duty assigned by some one senior to you. even time in the Corps not just rank. You remind them of that and let them decide how it is going to be handled.

That's easy...I'd tear him a new ASS in formation on-the-spot! He can try that "time-out stress card" if he wants to but I guarantee he won't be in the military much longer when I finish UCMJ actions!

I never have nor never will let that happen! HOOAH!

Remain calm; don't let your emotional reaction get the best of you. Instruct the Squad Leader to fall out of formation with the offender and bring him to you. Have a quiet conversation with the private about proper military discipline and respect for the chain of command. Ask him if he understands. Then instruct the Squad Leader to drop the private for 50 pushups and return him to the formation.
If the problem persists, it's time for Article 15 punishment.

Lock them up at "Parade rest". Get the rest of the detail out to their assigned duties. Get the PSG on the horn ASAP. Nature will take its course from there. Either "Joe" will have an epiphany moment or will be laying the groundwork for a pretty straight forward company grade conversation w/the CO & 1SG

how about stop being a bitch and choose someone else

I'd shine my boots with his ass.

This is, in no uncertain terms, insubordination. Definitions and possible penalties spelled out in UCMJ, Article 91. So...I'm right in line with Gunny Pepper (below).