Why is Leo Strauss critical of Historicism?

In answering this question we first of all need to establish the meaning of historicism. Broadly speaking, it refers to a theory which holds that social and cultural phenomena, including moral values, are historically determined, rather than absolute. Historicism as Leo Strauss understands it is closely allied with cultural relativism, the notion that there are no absolute moral standards. Nothing is right or wrong in and of itself, argues the cultural relativist; it is only considered so because of contingent factors such as culture, geography, and, of course, history.
The Aztecs, for example, believed that child sacrifice was not just right but a sacred duty. Today, of course, most people would be horrified at such a practice. The cultural relativist would agree but would go on to say that his or her revulsion was itself a product of their location within a specific cultural tradition existing at a particular moment in history. Good and evil; right or wrong; just or unjust; all of them can only be explained as historical phenomena.
Strauss's animosity towards historicism must be seen in the context, then, of his commitment to absolute moral values. In this regard, he is strongly influenced by the heritage of Greek philosophy, most notably Plato. Plato's theory of ideas (sometimes called forms) holds that there are absolute, supra-sensible entities which could only be apprehended by the intellect. As such ideas are absolute, they are timeless and unchanging. Examples would include Truth, Justice, Goodness, and Beauty.
In our individual cultures and societies, we can approximate to these ideas in our everyday practices, but at best we will only be able to come up with an inferior copy of them. For instance, in our various legal systems we will sometimes be able to deliver justice, but even in such cases it will never attain an absolute standard whose understanding can only be arrived at through years of study and reasoned reflection.
Strauss regards advocates of historicism as not being able to see the wood for the trees, as it were. So fixated are they on what is purely and radically contingent that they're unable to see the bigger picture of absolute standards of morality and what they mean for how we live our lives in the very societies whose workings they claim to understand.
For the historicist (a prime example would be Marx) no values can claim universal validity. The widespread belief that they do is a delusion, one that keeps us tethered to outmoded metaphysical concepts that tell us nothing about what's really going on in society. If we wish to achieve enlightenment, we need to throw off the shackles of our self-imposed delusions and recognize that only we as humans, historically situated in specific social contexts, can and should construct the system of values by which we then choose to live. As the dominant values in society are entirely contingent, they can be discarded and replaced by an entirely new set of values, based on the principles of constructive rationality.
Yet Strauss strongly contends that such thinking is far from leading us towards a more rational understanding of society; it actually has the opposite effect. Without any absolute moral standards, we are entirely cut adrift in society, unable to make any sense of the world around us. If moral values are merely historically contingent, then the only way to determine which are good and which are bad—or rather, which are more socially useful—is through some kind of conflict, be it social, political, or in extreme cases, military. In such a grim scenario, we are rendered powerless by the dictates of history. There is no final court of appeal to which we can turn, no absolute standards by which we may judge the dominant values of our time. All that we are left with is a morass of competing ideas, values, and philosophies which cannot provide society with any lasting stability.
The most serious consequence of historicism for Strauss is nihilism, which he defines as "the inability to take a stand for civilization against cannibalism." Historicism encourages the idea that we are all alone in a meaningless world without absolute standards of truth, justice, or morality. Given these conditions, we have no choice but to see ourselves as the playthings of fate, buffeted this way and that by the unstoppable tide of history.
We can try to make our own values, and this is certainly what existentialists like Nietzsche would recommend. But Strauss doesn't believe that such ready-made standards could ever endure, as what Burke calls "the private stock of reason in man" is woefully inadequate for this purpose. Hence it is all the more important that we acknoweldge the existence of moral absolutes, understand them, and live by them. Only then will it be possible to establish a society worthy of the name.