... I don't know whether the facts about how brains evolved over millions of years supports your statement or not. (the statement that other brains remained the same while other's evolved -- the same as what? Over what timer period? I'm not quite sure what you mean)
I know I've reviewed the Agricultural Revolution several times over the years around here. Consumption of grain - bread - created an explosion of cognizance, expanding exponentially symbolic reasoning and "rational" thought. This took place after the end of the Ice Age, +/- 10K years ago, and likely took place over 1-2 thousand years, but in that time humans went from living in caves to building walled fortress cities (Göbekli Tepe). A few thousand years later humans were building pyramids in Egypt and stacking dolmens to build Stonehenge in South England. In terms of evolution, this was racecar fast, and no other animals we can determine had any significant evolutionary adaptations quite so fast during that period of time.
There are some significant hiccups regarding human evolution. Aside from brain size (and resultant skull shape, and the resultant need for midwives at birth due to the enlarged skull and birth position - contrary to other similar size mammals), humans' canine teeth have modified to become smaller. Canine teeth are a traditional measure between predators and prey. Chimpanzees and Bonobos have canine teeth that would shred us, yet humans as the "apex predator" effectively lost their canine teeth. Humans developed sweat glands in the process of losing body fur, no other simian has sweat glands. None of these "adaptations" have precedent in the animal world.
Unique evolution isn't confined to humans, I can grant, but typically the animals held out for illustration of unique evolution include the likes of the platypus and echidna.
The find of Homo Naledi purposefully burying their dead is significant. Most recently I read Naledi is being dated about 200K years ago. The significance is that no other simians purposely bury their dead. Now, I have seen where a Chimpanzee troop would mourn the loss of a member, but no burial.
Add in the harnessing of fire, and flint / obsidian knapping, and human tool making quickly surpassed any other examples of tool making. Yes, there are those that point to a chimp or crow poking a nest with a stick, but aside from a rudimentary semblance of tool making there really isn't any comparison. Living in caves is not unique among animals, but decorating the caves is unique. While "art" can arguably be a practical function of many animals (nest building, spider webs), there isn't any plainly evident justification in a physical sense for humans to paint the caves.
Other aspects of cave painting really bring to the fore known psychological tendencies in humans. Ganzfeld Effect, Prisoner's Cinema and Sensory Deprivation illustrate the psychological gymnastics the human mind was already capable of, +/- 50K years ago. Blombos Cave in S. Africa illustrates humans decorating their bodies 100K years ago, Skul 5 in Israel illustrates considerate burial(s) 100K years ago. Both examples also demonstrate Ocher being used ceremonially, a practice that continued throughout the Ice Age and cave dwelling period.
Carved ivory / bone, and certain stones with a basic shape further worked by tools, were carved by the Cave Dwellers circa 50-60K years ago, older than the paintings. What symbolic purpose would such anthropomorphic figures serve? That question is leading, but what other possible purpose would such artifacts serve? No other animal carves figures. No other animal paints pictures. (Yes, I am aware of paintings done artificially and with human coaching by Bonobos and Elephants...show me any example in the wild.) I can even accept that the human evolutionary track is not going to be the same as that for other animals...yet there is nothing comparable anywhere else in the animal kingdom. Something about human evolution stands apart and outside of the commonly understood norms of evolutionary development.
My critique of Evolution here does not by default mean I am arguing in favor of Creationism, but it is seriously difficult to defend Evolution as the de facto and de jure natural mechanism applied to humans, at least not as we commonly understand that process and dogma.