Even if your dog is bigger than the coyote, the coyote will lure it away where the pack can take down the bigger dog.
I have personally witnessed this exact thing. We live in the country and routinely have coyotes cross behind the house in the pasture there. We had a Border Collie who thought it his job to "watch over" the back yard and pasture.
One morning I looked the window to see a group of three Coyotes just entering the pasture. The dog noticed them right away and started walking out toward them (still 200 yds. separating them). I knew the B/C wouldn't go all the way out there...but went to get my rifle just in case.
I did not call out to our dog...because I wanted to see what the Yodel Dogs would do (continue coming or flee). As soon as the lead Coyote spotted our dog (now sitting down about 50 yds. from the house) he immediately broke into a trot that brought him within 30-40 yds. of our dog. The Coyote then turned and made a big half circle back and forth.
The other two Coyotes hung back a ways and split off, one to the left the other to the right. Both just stood there watching the first one taunt the dog.
Finally, the B/C could take no more and loped out after the Coyote...which promptly ran over to a big brush pile I had pushed up in the pasture. It ran to the top of the pile and would come down about half way then go back up, while the B/C chased it. Only when the B/C got too close would it "snap" and "snarl".
In the meantime...the other two Coyotes moved in and flanked my dog. I could see this wasn't a "game" anymore and I moved out onto the back porch with the rifle. I called to our B/C but he pretty much ignored me (unusual for him). I thought about calling him off one more time but was afraid that if I diverted his attention away from the Coyote, it would attack him.
By now the other two were getting really close, their intention was clear.
I quickly sent a shot just over the top of the coyote on the brush pile (didn't want my dog to jump on it if I shot the coyote) and that worked, all the coyotes cleared out at break neck speed and the Border Collie didn't care for it either...as he came running back to the house all slinking and with his tail tucked half between his legs.
I have NO DOUBT those coyotes were trying to lure my dog out there (which they did) and purposed to "stretch him out" (all three attack him).
Not for food, they have plenty of that around here...but as matter of territory.