Whenever we needed to get one of ours in the carrier we had to set it up on end with the open door on top...in another room while one or the other of us were holding and petting the cat, then pick them up and walk into the room with the carrier and (most importantly) NOT LET THEM SEE IT until the last minute, whirl around and stuff them in like a slam dunk and close the door quickly before the managed to turn around in the carrier and start getting back out. They cooperated better at the vet because there were four or five of us to do the holding and stuffing, and they knew this was for the return trip home.

And ours were all pretty gentle and used to being picked up and handled!