What happens if you choose GLaDOS’ way in Portal 2

You can't catch him there: he will always fall to the floor. You can however pick him up after that happens.

Standing ready to catch!

Failing miserably...

But he's still alright!

Contrary to all the answers on here, it is in fact possible to reset your progress in co-op. Make sure you are the host (you invited your friend, rather than you were invited by your friend). Start a co-op game. Make sure you are in the hub when doing this.

Warning: This applies to both players. Make sure the other player is fine with you doing this.

Unfortunately, this doesn't work with ss_map. You have to be in a session with another player, and this will set both players' progress.

Enable the developer console in the options, then press ~ to open it. If you are having trouble, see this question. Then, enter the following command in the console:

mp_mark_all_maps_incomplete

You might see a weird message about DLC, but the command will have no other visible effect. Now, enter this command:

changelevel mp_coop_lobby_2

This will reload the lobby, and your progress will be reset at zero.

You can use this command to change your progress manually:

mp_mark_course_complete <course>

Whereas the number is the number of the course you want to unlock (have finished), minus 1. So to unlock course 1, use mp_mark_course_complete 0, to unlock 2, mp_mark_course_complete 1, and so on. This means that mp_mark_course_complete 0 unlocks course 1 fully, and will then open 2.

There is also mp_mark_all_maps_complete if you want to get Professor Portal.

Thanks to fail badp♦ for allowing me to waste his time.