Well you sort of can. You can sell a driver to another team and then after an agreed period buy them back again. There are a couple of problems with this:
If it's one of your academy drivers their wages are relatively low. If you sell and buy back later the wages will be a lot higher.
If the driver is trained by the other manager to a level higher than your manager level, the stars become red and you won't be able to bring them back into your team.
I imagine the reason that the game doesn't allow this is because it is open to exploitation by high level managers with multiple accounts "loaning" drivers from their primary to their own secondary account. Imagine how you would feel as a new player in Rookie and suddenly a new team rocks up in the league with Talent 20, Level 20 loan drivers.
