Let us suppose the holographic principle is indeed correct and that there is a (3+1)-dimensional quantum gravity theory that explains our universe, which has an equivalent description as a (2+1)-dimensional system. This simply means that the two descriptions cannot be distiguished so there is no physical experiment that could determine if we "actually" live in 3 or 2 spatial dimensions.
So your question touches on the question what physics can "actually" tell us about the world. The answer in this case is that two physical models in different dimensions are equivalently good models of the physical world. But that is all that physics can do for us, produce testable predicitions. So the question which one is the "actual" dimension becomes purely philosophical, from a physics standpoint there is no differenced between 3 and 2 dimensions.
why does everything in the universe look and behave 3D?
This is just the way humans interpret their perceptions and the names we have given to these perceptions. If there is an equivalent lower dimensional description of the world around us we can equally well say that the universe "looks" 2-dimensional.
Well, in conclusion you have to refrain from the idea that physics teaches us about what the universe "actually" is, it just provides models that predict thing we can measure. If two physical models yield the same predicitions, there is no way to distinguish between them. If one of these models is actually close to "reality" (whatever that is), is a philosophical questions.