Why aren't animals logical?

I had, a few years ago, a conversation online with a person who wanted to know why logical thinking is, at the time being, solely the domain of humans. Wouldn't animals benefit from logical thinking? Wouldn't it keep them alive in the tooth-and-claw world in which they live? Isn't their emotional-responses clearly counter-productive?
No, I argued. In the wild environment, animals do not have a lot of spare time for abstract thinking, nor the deep neurology that us humans possess to do it with. Confronted with a dangerous situation, the emotional response of "BAD THING RUN AWAY!!!" protects an animal far more than the thought of "Hm, that thing may be hazardous to my health, perhaps I should avoid it" proposed by logic.
Logical thinking involves a lot of meta-thought, of slow and considered abstractions, and this is a luxury that a wild animal does not have. That occasionally the "bad thing" turns out to be something completely harmless is no biggie if it protects you from the "bad things" that really are harmful. The cost of running away for no reason far outweighs the risk of becoming lunch because you weren't suspicious enough.
These arguments of course did not satisfy the other person. Surely our hypothetical animal would benefit from logical thought, he proclaimed. Logic would mean fewer false-alarms.
Perhaps, but unlike the "civilized" world we live in, our hypothetical animal is under time pressure. Predators can usually slightly outrun prey. The risk of failure is literally death. Logic would only benefit the animal if it could perform it as fast as emotions, in split seconds. Not even us humans, with our incredibly large and expensive brains, can come to a logical decision in less than a second. My friend has unfortunately anthropomorphized all animal-kind, imposing a framework of human psychology where it does not fit.
The other person unfortunately persisted in proclaiming that logic would benefit animals, so the conversation kind of stopped there. Yes, logic and deep thinking may be our advantage as humans, combined with tool use, but it relies on certain other features of us humans to make it worthwhile. A philosophical rabbit would be falcon-food.