Alan had some nerve to bring in such a big dog, although a cute dog, he didn't have the right to bring him into Charlie's house being Charlie wasn't too fond of having the huge dog there, but Alan always did what he wanted even if it was Charlies place and Alan paid nothing.
I think that Alan wants the dog back because it’s probably the only living creature to wake up in bed with him and not recoil in disgust while crying “WHAT HAVE I DONE?! I GOT TO STOP DRINKING!”?