Something that can't be explained by evolution, is : Conciousness and Free Will.
No matter how much you try to understand how it would form via evolution, it's impossible. First you have to understand the essence of Conciousness and Free Will. If truly you believe everything is but cause and effect, then you believe that you don't have free will; you have no freedom of choice, because your choices are but a consequences of the functions - you are a robot, only acting the way you are programmed to (along with many variables though for being able to adapt and learn of course), in whatever means is most beneficial to survival.
As for consciousness, it is about experience and a sense of self, which is absolutely inexplicable via any scientific theories we have.
What seperates something that interprets data, like a computer or beings that would have come into being through evolution, from us humans who can experience and feel, are not comparable, and many scientists who have studied the brain in-depth actually agree. I think the mentality is that they'll say they just haven't been able to explain it yet, though personally I think it's beyond comprehension.
I've had many debates concerning these topics, and actually at first I was debating Against consciousness and free will, but after unsuccessfully finding anything to counter many arguments I've come across, and just generally trying to understand my own way of experiencing and feeling, I think it's obvious that the theory of evolution is flawed, or at least significantly incomplete.
If you believe that there's only cause and effect evolution, then you're basically saying that you're a robot incapable of truly making your own decisions or actually experiencing anything, since cause and effect cannot take into account such things. I'd myself would be able to find arguments against this statement, but in the end none truly hold up if you understand cause and effect and how the Theory of Evolution prortraits it, or assumes it.
Certain aspects of the human mind are also not beneficial in any way, such as panic (not to confuse with fight for flight), and negativity in depression.. though it's hard to explain what I mean exactly, as this is a topic which I've discussed countless days about with philosopher friends. There are certain responses in both the human body and mind which are useful, but some are completely destructive and useless, we do not benefit in any way from it, and some of that I just call it plain negativity.. but there's other things as well. When you cry, you're not necessarily feeling bad or negative, but there's an added level of negative interpretation that can make you feel bad, and that leads to all sorts of destructive outcomes... but.. geh, too long a subject, maybe nevermind this, but I think many can agree that many things that happen with the human mind are only destructive and aren't beneficial to the individual, the race, or reproduction and whatnot.
If it's unclear why I'm claiming these things about consciousness, I'd have trouble explaining because it's very subjective; that is, experiencing can only be understood by individuals, and you can't really reproduce it or be sure that others besides yourself have it or understand it like you do.. same thing for feelings and free will.