I guess he knew he was sick and didn't want the boy to catch it.
Spoiler alert for them spoil sports out there! Y'all like spoiled milk, stop crying over it!

What the book says about Cujo should have been a voiceover in that scene. Not a dry eye would have been in the theater.

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it is explained in the book how Cujo is almost gone by the time Brett calls him and he recognizes his voices as the BOY who takes care of him and that is reflected in the movie sicne Cujo is ready to attack and growling until the boy speaks which is when the dog retreats.

I felt this was Cujo's last sense of compassion in the movie. He loves that kid and knows it would be wrong to kill him so he is battling with the good and evil aspect at that point before finally letting the good one win, for the last time in that movie.

He was just beginning to slip. He likely would have attacked or continued to show aggression had he not snapped out of it and began crying/whimpering.