Why would a dive operation need to hold your card after showing it?
They don't, so it is indeed curious. I have never heard of this before, and I don't know the precise details opf how people do it, so I am hazarding a wild guess.
There is a similar process among some car dealers. When you start discussing a possible deal at the early stages, they take your drivers license for some bogus reason or other and take it to someone in some back room. Later on, if the deal isn't going as you hoped and you want to leave, somehow your license is hard to locate. The person who has it is away from the desk, etc. That way they keep you in the store long enough (hopefully) to get you back into a buying mood.
Perhaps it is something like that. If you grow dissatisfied and want to switch to a different operator after a day of diving, you can't because you don't have your card at the moment and it will be a hassle to get it back.