Basically, we can take the stupid half of this argument as far as solipsism: "Nobody else has emotions but ME! You can't prove to ME that YOU have emotions, you humanoid meat robot!!!"
We can observe emotions, and model them with our big brains (even most of those that are 'sociopaths' or have certain 'autism spectrum' disorders can learn to), and conclude that emotions are at work, both in our fellow humans, and our fellow animals. Even animals have been observed to perceive emotions in others.
We can be 100% as certain that animals have emotions as we ever can be that any other human besides ourselves have emotions.
Lizards and birds and whatnot have emotions, too. Watch birds. Angry, territorial, etc. little bastards. Bummed out when they lose their nest, or their mate or their babies. I've watched with my own eyes a pack of quail escorting a gopher snake away from their young.
I have watched, again, with my own eyes, a raccoon stand in the middle of the road to stop traffic, for his friends to cross. Higher order 'thinking' in this example. One fearlessly stood there on his haunches in the middle of the road, staring at me, and his (maybe her) buddies all crossed when I stopped. Held his little paws up at me. Intent. Planning. Maybe even communication: 'Wait!' Those central California Sierra Nevada Raccoons are damned smart, and real problem solvers. Just ask anyone who has a trash can. I only wish I had a video camera rolling, at the time.
'Instinct' is 100% driven by emotions. You run because you're terrified. A predator hunts because it's hungry. It chases because of the excitement. It kills and eats for the pleasure. It's not an 'empty' needle on a gauge hitting a contact, even for house cats. They LIKE it. Capturing and murdering something is pure joy for them. Same as dogs, though they're usually a bit too strong to prolong the torment. Hungry, feral cats are more no-nonsense about it, but that's because they want the food more than the entertainment. If they become well fed (i.e. humans feed them), they don't stop hunting, but they do 'enjoy' the kill more. Then they try to teach YOU how. Share in the fun! I brought you a LIVE mouse (squirrel, lizard, bird, bat, baby opossum, etc.)! We can have FUN together!
Humans don't hunt because they 'have to'. They do it because they like doing it, too.