Mankind is unlike other animals in that we need external protection from the elements: we have no fur or feathers or hide to protect us from the cold or wet or sun. More than this: we have a sense of shame, an extremely important characteristic that spurs us to change and self-improvement.
I think this is a feature, not a bug. After all, when Adam and Eve discover that they are naked and they make themselves loincloths, G-d supplements their existing clothing with tunics made of ohr, skin. “And G-d made garments of skins for Adam and his wife, and clothed them.” Initially, nature does not protect us or cover us; G-d does that.
We are called to imitate G-d. So it is no coincidence that, even after the Garden of Eden, the principle of covering each other remains, but the responsibility shifts from G-d to mankind:
If you take your neighbor’s garment in pledge, you must return it before the sun sets; it is the only available clothing—it is what covers the skin. In what else shall [your neighbor] sleep? Therefore, if that person cries out to Me, I will pay heed, for I am compassionate. (Ex. 22:26-27)
G-d provides skin for mankind. And He calls on us to do it for each other going forward.
It is noteworthy that skins are also used in the text to protect the tabernacle from weather. The Torah has a simple lesson: animal skins are used to protect things that are capable of holiness. Nevertheless, both the tabernacle and people need to be separate (and cloaked) from nature in order to become holy.
P.S. The garments we made ourselves were from plants – and the garments G-d gave us were from animals. This is a foreshadowing of Passover grass+blood, and the mezuzah we use on doorposts which is also achieving holiness through combining animal, plant, and our own efforts.