The song was written before Wham even had a name, way back in '81. George took over the writing by the time the band were recording, so everything after that tends to only have his name attached to it.
The one thing you have to bear in mind above all else is that George's ego was the biggest thing in Wham. Bigger than Andrew, bigger than the name, bigger than their earlier, 'cheaper' hits.
By 84/85 George was almost embarrassed by the earlier material. He thought he was better than that & deserved better recognition. Meeting him in person, you'd think he owned any theatre he was playing at.
I had the misfortune to meet him once at the Lyceum in London, right as this record was being plugged, before it was a hit. He took the stage alone, dissociating himself from the earlier Wham incarnation. [The video had intercuts of another recording from there, idk whether that was recorded before or after this event.] George, even at the time, treated anyone else even performing the same stage as inferior. He was constantly surrounded by bodyguards [totally for show, as we were all in a secure, non-public area], & wouldn't speak to anyone. I spent the day instead with most of Culture Club & other lesser-known acts on that day. We all ignored George's ego & antics.
I did have the pleasure of working on another project with the guitarist & sax player from Careless Whisper, Robert Ahwai & Steve Gregory. Lovely chaps, great players.
George wanted adoration above all else.
That's why it's listed as being George Michael… ego.
See Wikipedia Careless Whisper for something closer to the 'official' story.