There are a number of claims that carnists make around pets that vary:
Holding onto an animal as a companion is no more "using" the animal than holding onto a child for which you are the guardian. It matters whether you are looking after the long-term well-being of the animal. People are looking after the well-being of their pets and intend to protect that animal from death until their natural lifespan expires; they do not do the same for farm animals.
Again, it comes down to the well-being of the animal. If service animals are being abused then the abuse itself is an immoral action.
Some have compared this to "raising backyard chickens". However, in raising backyard chickens, there's a few key differences. The first is that there's only about 1 service dog to 1500 people, rounding up, - in the US at least, which would, ballpark, correspond to about 1 egg every 10 years for people using the number they naturally live to 10 years and lay 1300 eggs (again, rounding up). This leads to the second difference, which is that then one needs to scale up massively if one intends to produce eggs on any level that avoids essentially going 99.99+% vegan. So you have to really start packing the chickens in, and then someone has to pay you for all the food you feed the chickens, and suddenly we're back where we started, which involves poor conditions for chickens caught in the animal agriculture system.
This would seem to be unlikely to be the case with service dogs given the scale of the demand for service dogs given that service animals are inherently in a 1:1 relationship.