For this, we might turn to Lewis' The Screwtape Letters. Screwtape write to Wormwood that after an initial period sweet bliss as a new convert, the time comes for the spiritual desert where God no longer holds your hand, where you must keep to or leave the path. For Screwtape it is the perfect opportunity for corrupting the human soul. But if the christian keeps to the path especially during those "desert periods," it pleases God the most.

So for the kids in Narnia, Aslan is telling them they must grow spiritually without the helping air of Narnia.

I’ve often wondered about this myself. I agree this is not about physical age because King Frank, Queen Helen, and Uncle Andrew were all adults when they entered Narnia. I think it had more to do with a personal maturity each character had to reach. All the characters were brought into Narnia for specific reasons. For Frank and Helen that reason was to rule and start a human population. Other characters like Edmund and Lucy were brought there so they could be introduced to Aslan and so they could know him in their own world. For them Narnia was simply supposed to be a chapter in their lives and once the learned all they needed from Narnia that chapter ended. I think for them Narnia was supposed to be like college. It’s a very important part of many people’s lives, but it’s not meant to last the rest of their lives (although I’ve known people who have tried to stay forever ). People are supposed to learn what they need to and move on to the next stage.
It’s also interesting to note that this growing too old for Narnia is not the case for all of the characters. Frank and Helen not only come to Narnia as adult, but they do stay for the rest of their lives. Also, in LB

I think Aslan wanted them to continue their mission back in England- or wherever they chose to go.

And also that now they are old enough to reason and make wise choices (Aslan hopes). They were given free will. They were given the tools. It is up to them to use them for the right reasons.

I think Aslan expects them to finally know who he is in their own world, no matter their fate would be they are at the right age to try to see who he is in their world. Of course in the books the children were very much younger then the cast in the films.

In the film PC it seems Susan learned nothing and Aslan just wanted to haul her out of Narnia never to come back because for one, he knows she'll drift away from him in both Narnia and her own world.