Hitchens called into question one of the basic threads of the human fabric, religion. For many, the idea that religion is not only man-made, but harmful and not necessary is one they cannot accept or even stipulate for a moment. His methods of argument were clever. For example:
Deists believe there is a an intelligent designer behind life, yet...
Of all the living creatures that have ever existed on earth, 99.9% of them are now extinct.
Humans in their current form appeared around 100,000-200,000 years ago. For 98,000 years, life was full of fear, death, pain, fighting, hunger, life was short, there was no understanding of lightning, earthquakes or microbes. In short, life was filled with pain and heartache and misery.
After 98,000 years, and the failure of 99.9% of his designs, the Designer decided that the best way to put an end to this suffering and make things better, was to select and torture a Middle Eastern man.
The strength in this argument is that it seriously calls into question the more probable of the two Christian god-types (deism and theism). So, if the idea of a designer is completely unsupported, the even less likely is it true that there is a personal God who loves you.
Another aspect is the idea that a human can know what God is or wants. According to Hitchens, even if it were true that God as Christian define him exists, there is no way a human could possibly access what God wants or knows, or to understand anything about him. Thus, for sanctimonious Christians to claim that they "know" what God wants is absurd. Each of these people is a refutation of God on Hitchens' view. To explain Hitchens' thinking on this further, think about how science "knows" other species. They have experience with them in a way that is observable and base claims on evidence and facts (behavior patterns, chemical analyses etc.). This is not possible, by definition, of God.
Hitchens had great arguments, which for many, are strong evidence that there is no God. Even those who are not convinced are forced to concede that they have a lot of argumentative work to do. Trying to prove that God exists in addition to his wants and nature is a tall order. To many, it seems obvious that the simpler story is more likely true. There is no God. It is just a story made up long ago when there were no other explanations for life's questions.