The balancing factor of this would normally be the age of the NPC teacher.
The older the NPC, the higher their skills, but the sooner they will have to start making those winter aging rolls and the sooner they will die (unless you invest in making them a longevity potion).
Ars is built around the concept of long running (in terms of game time) campaigns where the age of your NPCs do become a concern. As a covenant transitions from Spring to Summer and Mages spend years in their labs perfecting their longevity potions, their covenfolk steadily grow old and die. We have recently had a series of adventures based on finding appropriate apprentices for our irreplaceable grogs, so that when they die, their skills don't die with them.
A player asking for an Immortal Forest as their teacher is trying to find a way to get around one of the implicit laws of the setting, so Rule 7* should apply.
* Rule 7, generally defined as "Don't take the piss.", see the definitions at the Urban Dictionary.
To price up the cost of an Immortal forest teacher, try stating up an equivalent library, and then give a discount for the only one person in the library at once flaw. You will almost certainly find that route makes it far more expensive than your player is prepared to pay. Then you can work with them to provide a useful normal teacher that is within their points budget.
You could even encourage that by suggesting that they can reduce the cost by giving the NPC a low teaching score. You can then make this poor teacher a story element. As they get more experience teaching they will steadily get better. Also, any seasons when they are not teaching, they can be learning - making them even more valuable as a teacher. The immortal forest would essentially be static, it would learn slowly, if at all.
Either way, there are many ways to make a character element like this an interesting element of your covenent. I created my companion in my current Ars campaign to be useful as a teacher. He started out as just the covenant librarian, but has gone on to create a religion and is starting to spread it around our homeland.
Another option is to allow your player to take this immortal forest as is, but only on the condition that it has a flaw he doesn't know about. Maybe the immortal forest learnt everything it knows by murdering and absorbing people with those knowledges. Maybe it is a demon trying to corrupt the innocent magus with easy knowledge. There are many options for you to play with, and the player has given you Carte Blanche to mess with their PC in many and varied ways, especially if they know how much cheaper their Immortal Forest is than the one-person library. *8')