Should a Soldier be chaptered for failure to qualify with their weapon?

No, we are not going to get rid of soldiers because they can't qualify with their assigned weapon. Instead, we should look at the "whole or complete soldier concept" and evaluate retain-ability based on ALL soldier and MOS skills & attributes. Not just one thing. I agree with your way only under certain circumstances.. like if they were infantry or in a combat environment. I just don't see the value in retaining expert marksmen or pt studs in a garrison environment. We should look at everything, especially if they are proficient in their MOS. Or.. if they enjoy pulling duty, they are a keeper (joking)

I just assumed it was a given...

I see lots of posts on this thread comparing it to failing common tasks such as Land Nav, Radio communication, etc. I don't agree with this. Rifle/Pistol qualification is as basic as it gets in the military, particularly Army and Marines. If it has been deemed the soldier received proper instruction and range time. And still can't pass, then YES, get rid of them. Simply put, as simple of task that shooting seems, some people just can't do it, for whatever reason. I went through basic in '86 when the thought of unconventional warfare seemed so extreme, it wasn't even discussed. These days, experience shows us that ANYONE is a viable target, whether a grunt on the street, or a supply clerk in a supposed secure zone. Quite frankly, if you can't shoot, you are a danger to yourself and your fellow soldier.
With all that said, I do believe there is not enough emphasis on weapons training. Most units qualify once a year and that may be the only time hey fire their weapons until next qualification. Due to drawing weapons for alerts and field exercises, I think we spent 20 times more time cleaning our weapons than shooting them. I don't know who ultimately makes that decision, or if it's budgetary reasons (I know each unit has a budget), But one would think that in order for a military unit to be considered "combat ready", they should at least know how to shoot. But nope; in our unit, a combat engineer unit, there was more emphasis placed on drip pans in the motor pool and having your boots spit shined ad uniform starched and creased than there was in marksmanship.

Yes. No differently than APFT, weight, or any other standard. Unfortunately only TWO standards in the Army seem to get the attention when it comes to chaptering. Why? Because they have become easy to process as most chains of commands are well versed in it.

I appreciate the dialogue we have going on here. There is a lot of interesting perspectives on this. Keep it up.

Air Force Qualifications are tracked electronically. As a Former NCOIC of a Marksmanship Instructor Section, I had to document failures and how many times each person failed. I think it is still three failures and you are re classed. Some are already at the lower end of the minimum score nec. For them they are dropped from the AF. The failures have to be in a roll. If they meet the minimum standard their clock is reset.

Can you graduate from basic training if you don't qualify with your weapon?

One of the greatest soldiers in history refused to even carry a weapon(Desmond Doss). There’s more to the army than just killing and destroying the enemy. A soldier can be an asset for their skills in mechanics/maintenance, medical, logistics, transportation, etc. There’s plenty of people that want to break things but not enough people that want to fix or repair. That’s why we have to rely too much on civilian contractors.

Is it really in the public's interest to throw out a soldier (with an Honorable Discharge mind you) because you don't want to take the time to conduct training? Do you have any idea how much it costs taxpayers to fully train/clothe/pay/take care of soldiers? I'll tell you...for a brand new, untrained recruit it's about $15,000 straight out of the box. Then once they are fully trained, equipped, and deployed, it is about a half million per year per soldier. Still want to throw all that money away when a couple of intensive training sessions will fix the problem?

Separation for Unsatisfactory Performance Chapter 13, AR 635-200