I've debated a handful of times, and the initial approach comes down to misunderstandings about how animals communicate consent compared to humans and animal motives for sexual interactions.
Most of the people I've debated with were religious about the idea that consent needs to be verbal, and were dismissive of the idea that even humans partnering with each other could use body language and other overtly suggestive behavior to communicate sexual interest and safely initiate sexual intercourse. I could only chalk it up to lack of sexual experience on their part, or lack of forethought into the argument they were trying to make.
When using an example such as a dog mounting a human and actually initiating intercourse themselves being a way of communicating consent, they would sometimes double back to the misconception that animals only have intercourse for reproduction and that the human was taking advantage of their instincts for their own pleasure, as if the animal wouldn't mount if it knew that relations wouldn't result in pregnancy.
After explaining the hormonal, physiological, and psychological similarities between humans and other animals to clarify that animal sexuality is usually motivated solely by the pursuit of pleasure, if they're willing to concede that their other arguments were ridiculous, it usually comes down to "it's gross and I don't like it". When all else fails, there's a sorry tendency for them to believe and express that they don't need to come up with a winning argument because zoosexuality is wrong by default without any need to prove it.
They would also occasionally argue that the power difference could make the animal feel pressured into sexual intercourse, or that memories of the sexual interaction could traumatize the animal later on, but animals have the privilege of being able to enjoy sexual interactions at face value without susceptibility to the more complex social and psychological capabilities that make these things possible in humans. An animal simply cannot be "taken advantage of" in the same way as a human when those venues of psychological harm do not exist, and assurance of safe mutual enjoyment with animals both immediately and long after is actually greater than humans in general who have the potential to stress over past sexual interactions because of the greater social and contextual considerations available to their thought processes.
The simple answer to your question is projection and anthropocentrism.