Some things that animals can easily do that AI can't do or can't do very efficiently at the current stage: vision, balance, proprioception, gauging progress towards a goal and adapting the plan of action on the fly, selecting the proper goals from among many possible goals (self-direction), reading and responding to the intents of other agents in the environment, reasoning from first principles about things like what presents a danger or an opportunity, dealing with uncertainty in a fairly reasonable way, etc.

These are things that almost all animals, and certainly all higher order animals, do automatically. They can do these things while also being mobile and operating on low energy. Robots that can do some of the vision, balance, and proprioception parts, for example, still have to be tethered to a power source or carry around a massively heavy battery in order to power the hardware required to make the rather intensive calculations, whereas humans can do all of this and much more (and do it much better) while running on only a tuna sandwich and a glass of water. So part of this statement about the relationship between AI and animals is about total capability but a large part of it is also about efficiency.

Computers have to make explicit the computations that nature has spent billions of years refining in relatively common chemical systems. We are not yet anywhere near the subtle genius of nature in the complexity and generalized success of our designs, even if in some special case uses we have been able to complement her weaknesses (such as performing explicitly mathematical operations and applying those to a vastly increased memory storage).

To answer your question though, we would only create AI that explicitly thinks like an animal when we think of some fruitful (probably profitable) application that requires it. AI can be designed in billions of different ways and none of them necessarily need to resemble anything found in the animal world. AI should and probably will be designed to play to its strengths and complement our weaknesses.