"What can be asserted without evidence can also be dismissed without evidence."
This quote by Mr. Hitchens has become a minor internet meme, most often in the form of a demotivational poster with the header "Hitchens' Razor" underneath a photo of an old-fashioned straight razor. This is a reference to the distantly related Occam's Razor. Unfortunately, it is often treated as an argument (usually for atheism) rather than what it is -- an offhand dismissal.
On a straight-forward reading, Hitchens' Razor can be taken as a basic statement of the nature of science and the scientific method. Science is a meaningful system of justifying of our beliefs because it gives us explanations that can be tested -- in other words, science gives us evidence. This is an excellent justification for aligning our beliefs with those endorsed by the scientific establishment, and is an even better justification for learning how scientists justify these beliefs.
But this razor is horribly wrong.
I can assert anything without evidence. So can you! "The earth orbits the sun", for example. Of course, if I fail to provide any evidence for this claim you might well dismiss it out-of-hand, as was done for a number of centuries, but dismissing it thusly will not get you any closer to the truth. The simple fact of my asserting that the earth revolves around the sun should not put that hypothesis in a privileged position, but it should remain on equal footing with alternative hypotheses until one hypothesis does get some evidence to favor it.
In other words, Hitchens' razor, in its current form, is equivalent to stating that if one lacks evidence favoring a given hypothesis, you can arbitrarily ignore any possibility you like -- or in other words, pick one you like and ignore the others. This is painfully against the scientific method. The sciencey thing to do is to find a way to test the hypotheses!
While the razor is not true, it is truthy. It might be interpreted as a well-meaning simplification of the statement "a hypothesis that does less to explain the observed universe shall not be privileged above one that explains more". But this would require that one does at least a rough estimation of the evidence available to each hypothesis. In other words, it should only be dismissed after you have evidence that it should be dismissed.
Is should be noted that this idea is not by any means unique to Hitchens. His razor is basically a translation of the Latin proverb quod gratis asseritur, gratis negatur, which has been muddying the logical waters for centuries.