The general reason to reject non-evolutionary theories of morality, just discussed, is the fact that the lineages of their morally-observant individuals would be eliminated by natural selection, which would make it a mystery why we still care about morality at all. But particular non-evolutionary theories have other flaws as well.
For instance, utilitarianism and other forms of consequentialism are still taken seriously. The trouble is that there is literally no evidence that any consequentialist principle is true. There never has been and, after centuries of failures to produce any, there is no reason to think that there ever will be.
Jeremy Bentham invented modern utilitarianism in the 18th century. There are many problems with the case he made for it.
Bentham attacked a straw man to make his own theory appear credible in comparison. His bete noir was intuitionism. He maintained that there was no way to distinguish reliable from unreliable intuitions. He ignored the intuitionist explanation that intuitions were unreliable when they were contaminated by error or ignorance with respect to material facts, that is, non-moral facts.
Utilitarians like Bentham are in no position to ignore or reject the intuitionist explanation because utilitarian judgments can themselves be contaminated by the same kinds of error and ignorance. You cannot maximize happiness unless you believe truly about what increases or reduces happiness. Utilitarians have the same problem as the intuitionist, and need the same solution, namely, the rejection of contaminated judgments.
The contemporary utilitarian Peter Singer has proclaimed that we should reason with ourselves. But there is a difference between using reason to apply a utilitarian calculus and using it to justify its application. It is easy to do the former but impossible to do the latter.
Utilitarianism has results that people instinctively reject. Most people believe that we should direct a runaway train so that it kills one stranger rather than five. Most people also believe that we should not throw a fat man in front of the train to stop it. Even if we could convince ourselves that we should sacrifice the corpulent individual, we cannot convince ourselves that we should throw ourselves, let alone our children, in front of the train. But utilitarianism, to be consistent, must be just as insistent that we sacrifice ourselves, or our children, as it is that we sacrifice obese strangers. (In contrast, we will see later how evolutionary intuitionism explains our instincts in such cases.)
The fact that utilitarians are committed to sacrificing themselves or their children for strangers also puts them obviously at odds with evolution. The commitment would reduce their viability or fertility – their fitness – and utilitarians need to explain how morality could persist in an evolutionary world if their theory were true.
We should be able to find flaws in other non-evolutionary theories as well. But there is no reason to try. Questioning utilitarianism is worthwhile just because intuitionism will be rehabilitated later – the theory argued for here is called evolutionary intuitionism, after all.