Animal reasoning actually is reliable, by degrees. The smarter an animal, the more reliable its reasoning powers are, as science has confirmed, and this is always associated with physical enlargements in key areas of the brain, which in humans are far larger than in any other animal. It is thus to be expected that our reasoning abilities should be far more effective than those of even the smartest nonhuman animal, and this prediction is confirmed in practice, as we can solve problems, plan, anticipate, and remember, analyze, and communicate information far more effectively than apes, dolphins, crows, elephants, cats, or any other animal of notable intelligence. That's why we have a civilization, with technology, science, business, and government, and why we were able to invent mathematics and logic.
What gives us this remarkably advanced reasoning ability? A highly evolved complex brain, which is essentially a natural computer employing synapses, biochemistry, and electricity to compute information. Everything we do, is just more efficiently done than some comparable ability found in other animals. In the language of computers, we can do more, because we have more processing power and thus can develop and run much more complex programming. We evolved this ability because it gave us a new ecological niche we could exploit to gain an advantage over competing animals (just as wings did for birds, or gills for fish, or flexible rib cages for small cats), and therefore as we started exploiting it, natural selection favored its refinement over hundreds of thousands of years, until it became so refined it could produce a civilization.