Since the taxonomic classifications are based on the evolutionary theory, one can get a bit lost in the definitions, but according to the dictionary, an "animal" is "a living organism which feeds on organic matter, typically having specialized sense organs and nervous system and able to respond rapidly to stimuli." So according to that definition, we are biological animals.....but there is a lot more to us than meets the eye.
Think of the ways in which humans differ from animals......e.g.....in language, we have verbal communication, body language, facial expression, hand gestures and the written form. Animals have their own means of communication but none have the same variety of communication as humans do.
Intelligence in humans is more advanced than in any other "animal". We can build and invent structures that are enormous and imposing, but we need to learn the skills. Animals are programmed by instinct.
We also have the ability to plan based on imagination. Only humans have a concept of past, present and future, so they can use information from the past to plan a future activity based on what an imagined outcome might be. Compared with the instinct that drives animals, humans alone being made in the image of their Creator can reflect his ability to foresee certain eventualities.
Instinct might prompt a squirrel to store food for the winter, but he does not consciously do that. He is programmed to keep himself alive through a harsh winter by doing so.
Birds, whales and butterflies migrate, but they don't know why.....they just know that they must do so by the instinct that drives them. How do they know where to go?
Spiders spin webs using a material secreted from their bodies that acts as a sticky net to catch food.
Science is trying to duplicate the strength of a spider's web in a rope that, if it was of equivalent strength, it could catch and hold a Jumbo Jet in mid flight.
Birds build nests of the same style and shape as their parents, yet no one teaches them how to do it, and none of the babies was alive when their parents built their nests....programming needs a programmer IMO.
What about the Arts.....think of the ways humans can express themselves through art, music, poetry, literature and theater.
Think of the ability to copy a scene on canvas that is transferred from the eye to the brain and then to the hand to replicate the scene with a brush and paint.......or the ability to create music and the multitude of instruments that humans have invented to express their emotions with sound. All of the Arts are a reflection of the Creator and his abilities bestowed on us as his representatives on earth.
These things make me know that we are much more than just animals.