By chapter 7, the pigs are firmly in control, even though they are not the strongest animals. This is because they use the dogs as enforcers. Napoleon sees Boxer pinning the dog as a threat to his power.
Napoleon and the pigs use the dogs as their private security force. Napoleon’s power is cemented from the fact that the dogs intimidate the other animals. When Boxer pins one of the dogs, this is a thread to Napoleon. Napoleon does not like threats to his power.
When three of the pigs “flung themselves upon Boxer” (ch 7), he defends himself but then looks to Napoleon to tell him whether or not to kill the dogs.
Boxer looked at Napoleon to know whether he should crush the dog to death or let it go. Napoleon appeared to change countenance, and sharply ordered Boxer to let the dog go,whereat Boxer lifted his hoof, and the dog slunk away, bruised and howling. (ch 7)
Napoleon’s countenance (expression) changes because he sees the other animals respond to Boxer’s strength. He cannot have Boxer as a threat. The dogs, not Boxer, must remain the threat.