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[GoT] Why wouldn't they teach Hodor how to fight?

GoT S6 Ep2 Spoilers:

So in the "flashback" where Bran is shown his father, uncle and Lyanna in the courtyard where they are about to have Hodor, who can speak and is intelligent enough to comment he knows Neds(?) fighting style, spar we are interrupted by Old Nan.

She says Hodor will never be a fighter because he's a stable boy... as she leads a hunched over child that is still taller than Winterfell's guards away...

How could he not at least be expected to become a foot soldier one day? It doesn't take a military genius to know someone of that size with some half-decent training would be a great asset as a guard or otherwise. 

Would the Starks have really squandered such a gift?
gpt
We'll never know because Hodor turned simple. It's possible that if that never happened he would have eventually become a man-at-arms just by sheer necessity.  But most men-at-arms and soldiers you see are just farmers and craftsmen drafted to fight. Remember the time Aria found a group of Lanister soldiers and they were just normal dudes and Ed Shereen?

Now, being trained to fight at a young age was the privilege of the elite. They didn't have to help their parents tend the crops and care for animals. They were given proper book learning, lessons on leadership, and taught to fight. That's why all these noble types are so much better at it than most normal people, they've been doing it longer and with proper instruction.

When Hodor's mom is telling him to get back to work she is telling him he is not a Noble who can while away his hours with frivolous things like swinging a wooden stick around, because he has work to do. Unlike Robb, Jon, and Theon.