"Survival of the Fittest" implies a competition to the death, a universal sibling rivalry in which altruism, cooperation and brotherly love have no place in the behavior of a viable species. With that attitude the notion that the evolutionary advantage of the human species was the ability to cooperate in complex and subtle ways was simply not in the repertoire of evolutionary biologists. Even if they had been able to think in terms of the vector spaces so common in modern physics it would have been too radical to see that evolution favors cooperation.
The notion of evolution, that the living beings we find today developed over time from different living beings is, and has been for the last century, a bone of contention between the religious and scientific establishments. The way the concept of evolution should be applied to human beings, individually and in social groups, has been very dependent on social conditions. The current positions are that the fundamentalist religious groups want the Jewish creation myth taught as science, and the scientific establishment insists that the notion of "survival of the fittest" is scientific fact.
In fact neither of these dogmatic positions is tenable. There is no particular reason why we should choose the Jewish creation myth as more scientific than the creation myth of any other religion; and even the creationists have been able to make serious arguments against "the survival of the fittest" as a scientific principle. But the fact that both positions are too weak to defend easily has made both sides revert to dogmatism.
In fact it makes the most sense to start from the beginning and take a fresh look at Darwin's notion of natural selection.
Ever since Darwin proposed the idea of evolution by natural selection there has been a running battle between the Darwinists and the churchmen.
After the atom bomb science was in the ascendant and popular theology lost prestige. From the late 1940s evolution became the preferred dogma in the educational field. In the 1960s, when the scientists lost face because of the environmental movement (and their own arrogance), the opponents of evolution started calling themselves "creationists" (rather than sectarian fundamentalists) and found a market niche in anti-intellectual populism.
The net effect is that on one side are creationists claiming that the past history of the earth is as described in one or another version of the Jewish creation myth; on the other side are Darwinists claiming that we evolved by a process of natural selection summed up in Spencer's phrase "Survival of the Fittest".
Neither is correct, but they are so emotional about it that they can't see the simple flaws in their argument.