I myself believe that evolutionary theory must be the backdrop for any explanations regarding human behavior, but cannot be directly applied to humans and their historical journey because humans do have conscious intentions.
I found this reference to "conscious intentions" rather interesting. What Mazlish seems to be saying is that human beings make conscious decisions to do certain things; they are not entirely driven by mere instinct. The problem--as I see it--is that "evolution" (by which I assume he means neo-Darwinian evolution) cannot explain why human beings are able to make conscious decisions; if we are merely highly developed animals, how can it be that we have escaped the power of our instincts?
What this quotation shows, I would argue, is how even highly intelligent people fail to recognize how their intellectual commitment to Darwinism leads them to hold to logically inconsistent beliefs. Of course, Mazlish was a historian, not a philosopher, but isn't strange that even he could not see the contradiction here? Truly, in the case of many well-educated people, belief in Darwinism resembles nothing more than a sort of "blind faith."
Image of Charles Darwin from Wikimedia Commons