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

Really!?? What's the question here?
As Former E-1 Shithead that made E-6, then OSC'd up to 1Lt in Artillery, Armor and finally in attack helicopters I will say this . You follow all lawful orders of your superiors, thus is the military not some mamby pampy civilian job. Discipline is for a reason and not optional. I'm a little tired of hearing all this personnel management bullshit that's invaded and infected the military, leadership is what counts, earned respect of authority is everything, and so are shit assignments sometimes. The snowflakes need to get out and stay out !!!

Back in my day he would have been picking his bloody face up off the floor. I'd need to research current regs but that type of disrespect and failure to follow a lawful directive would need to be at least and article 15.

Talk to him in private and see if something else is bothering him. If he continues to be defiant you immediately inform your superiors and Company Commander. Demote him to private E-1, and have the M.P.'s take him to jail.

Understand I am a Coastie, so terms may differ. First establish control. "Belay that!" Dismiss the rest of the group, ordering the person in question to stand fast. Afterwards, some fan room counseling would be in order. Sometimes discipline can best be handled outside of official channels. Sometimes more official actions are required. On my last unit, I was Electronics LPO and had a problem child. The previous LPO had taken the official route, placing him on report on several occasions. When I reported aboard, I had discussed his situation with the Operations Officer, an O4 who was my direct superior. (Before someone says something yes, there was a more junior officer or rather junior officers assigned as Electronics Officer, but they rotated on a regular basis and stuff like that I went right to the Operations Officer.) After being briefed on the past issues, I said I would like to try and handle this on a more informal basis. We did have a few Fan Room sessions, many sessions of extra instruction, some special work details, etc, but in the end, the CG lost a problem child and gained a squared away sailor.

He should get his ass kicked in front of everyone so it's a lesson to all, however with the pussification of todays military most commands or branches wouldn't tolerate it. Glad I'm retired.

Wall to wall counselling session
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I never heard of anything like that happening in my day. But that was thirty years ago. Punishment would have been swift

When I was a Sgt I'd tell him to step out of the formation, come to the POA and wait. I'd dismiss the platoon, put him in a vehicle and drive to a nice remote place and change his attitude.

Is there any reason why folks would question your leadership? If you are a outstanding and upright NCO. Explain again that the detail was a order. And if he didn't want to follow the order. Take him over to the 1st sgt.

But are you in the a grunt unit or admin type unit. That might make a difference

I've been lucky thus far, but I've had fellow E5's do this to me.