Do you start the game with the drive in the CD player ?
The way you describe the issue, it seems that you start the game before the CD is in the drive. In that case, the game will obviously require it to continue.
Even so, I have a game for my daughter that requires you to start on one disk, then put the next one into the drive BEFORE being able to play. Kind of like they want to ensure you have both disks before authorizing you to play.
For a kid's game, I found that quite trusting (not!!).
Bottom line is, if the game is multi-disk, then you have to learn how the game wants to start up. Although most 2-disk games let you start on the Play disk (like Diablo II), some want you to start on the Install disk. Imperium Galactica II (4 disks) wants you to start on the disk of the race you choose to play (one of three). Dungeon Siege (2 discs) will actually let you play on either one, as will Battlefield 1942 (although the latter will display a warning if you use the Install disk, it will still work).
As you can see, it is very much a case-per-case thing.