I think the issue is the Primer.
I don't think X truly understood what he was giving them: he thought they would be educated, sure, but looking back from a more mature perspective, the sort of education the Primer dishes out is serious stuff.
The Mouse Army is doing it's own thing.
They're a bunch of self-actualizing badasses, not following the sort of simplistic ideology of the Fists.
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Remember that a key part of the Primer - kept secret by Finkle-McGraw - was that the book was intended to be "subversive."
Dr. X didn't know this; also, toward the end of the book, he explicitly says he regrets educating all the girls via the book, presumably because they are not cooperating.
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All these answers miss the point that when Hackworth is being sentenced by Judge fang he subverts the books to be linked to the missing primer (the one owned by Nell).
"At this point, John Percival Hackworth, almost without thinking about it and without appreciating the ramifications of what he was doing, devised a trick and slipped it in under the radar of the Judge and Dr. X and all of the other people in the theatre, who were better at noticing tricks than most other people in the world.
“While I’m at it, if it pleases the court, I can also,” Hackworth said, most obsequiously, “make changes in the content so that it will be more suitable for the unique cultural requirements of the Han readership.
But it will take some time.”
"
He basically takes a subversive book
makes it more Chinese and respectful of authority but he makes the authority the owner of the missing book.(Even
Hackworth has no idea who owns this book at this stage.)
Thus the hunt for Princess Nell by the mouse army.
"Hackworth sat down across the table from Dr. X.
A young woman padded out of the kitchen on silk slippers and gave Hackworth his own tumbler full of green tea.
Watching her mince away, Hackworth was only mildly shocked to see that her feet were no more than four inches long.
There must be better ways to do it now, maybe by regulating the growth of the tarsal bones during adolescence.
It probably didn’t even hurt.
Realizing this, Hackworth also realized, for the first time, that he had done the right thing ten years ago."
So the girls will become Leaders of a new way, with out the foot deforming etc, but with the use of the seed.
"The provisional commanders of her divisions stood foremost, as did her provisional ministers of defense, of state, and of research and development, all of them bowing to Nell, not with a Chinese bow or a Victorian one but something they’d come up with that was in between." The book of the seed is inside Nell's Primer at the end and being worked on by the drummers even as they remove Miranda from the Drummer community. "
“Hackworth is the Alchemist,” Nell said, “and he is using the wet Net to design the Seed.”
"
As for them both leaving the Middle Kingdom they attack the fist checkpoints while Hackworth is watching and tie them up.
This is after they discover their leader in the Primer after Nell breaks the last turing machine and the land beyond disappears.
So they meet Nell in the book get turned into humans in their primers and then in real life head to where Nell is as an army of followers.
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The very beginning of the book, where Lord Finkle-McGraw and John Percival Hackworth discuss the idea for the primer, made clear that it was intended to produce not just educated girls but subversive ones who can think for themselves and take charge.
Then the first set of orphaned girls got old enough for the high-tech "foot binding" process to be used on them.
We know only a few of the oldest girls were subjected to this because they are the ones being carried by the army on the march.
The girls as a group must have seen the results of this crippling and oppressive procedure after the first set of girls got bound, issued a collective HELL TO THE NO, and decided to get off their boats and go find Princess Nell.
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It seems that they are meant to represent the melding of two cultures.
The Boxer Rebellion was lead by The Society of Righteous and Harmonious Fists, and was anti-foreign.
If the novel draws from this event, then we can see this as antagonistic towards the Victorian principles and "colonization".
From Wikipedia : "The Confucian solution of the Primer was hierarchical, while the Victorian was highly individualistic."
So the Mouse army, can be thought of as the combination of the best elements of both cultures/worlds.
On top of this, the networked Primers form a sort of communication network for the Mouse Army (similar to the Drummer network).
The Fists are going to try to hold back this new group and use them for their own benefit.
The only way to combat this is through... combat.
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I have just finished rereading  Neal Stephenson 's  The Diamond Age  for about the fourth time and am still confused about the ending.   The part that is confusing me is as follows:   Both the Fists and the Mouse Army come from the Celestial Kingdom yet they seem opposed - surely Dr X would have wanted the Mouse Army to support the Fists. Maybe I misunderstood?
The ending of The Diamond Age
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 The Mouse Army, can be thought of as the combination of the best elements of both cultures/worlds.  The Mouse Army was doing its own thing and the  anti-foreign Boxer Rebellion  was led by The Society of Righteous and Harmonious Fists. The mouse and fist armies seem to represent the melding of two cultures, thus they were intended to be different and appose each others views. For instance the Righteous and Harmonious Fists could be seen as "anti foreign" while the Mouse Army was perceived as a culture with the best elements of both worlds. 
The mouse and fist armies seem to represent the melding of two cultures, thus they were intended to be different and appose each others views. For instance the Righteous and Harmonious Fists could be seen as "anti foreign" while the Mouse Army was perceived as a culture with the best elements of both worlds. 