I mean think about it. They stopped working together after Nightmare Before Christmas. Tim Selfinserton is known for really connecting to his characters; and for Nightmare, Danny insisted on being Jack because he saw so much of himself in him. Considering that Tim kept putting off writing the script (and then ended up not doing it lmao) and for some time the only words on paper were Danny’s songs, and parts of the film were shot before there even was a script. The fact that Tim wasn’t directing and the “script” they were using was Danny’s (who Tim didn’t respect) must’ve been a blow to his ego. Tim’s characters are him, he couldn’t handle Danny’s control over Jack who he (Danny) also saw as an extension of himself. You can see that in the film, as Jack isn’t the typical Burton protagonist, most notably in the scene where he realizes he was wrong and goes and fixes his mistake instead of whining about how no one gets his art and running away. So they didn’t speak for three years because they were doubles of Jack Skellington.