I will second that. Your log book is 'personal' and should not be left with anyone. If CASA want it, they need to put it in writing, and issue a receipt when you hand it over. That does not prevent the CFI of the flying school, or a CASA Inspector or an ATO requiring to sight it (and sign it where necessary) while checking that your entries are kosher.
A lot of students are a bit bamboozled by flying school demands. You are the customer so you would be surprised at what you can negotiate. Capping the amount of ground time you are charged for during ATC delays, for example.
If they won't play, take your business elsewhere.