As Richard Dawkins would describe the movement. These atheist are set out to destroy religious faith. Why? They believe religion promotes violence, and generally is a major bump in the road for the progress of mankind. The movement is in no way a promotion of violence towards theist, merely, just a movement of intellectual battles in debates, articles, books, and so on, until a theist can no longer intelligently say their is a creator.
As the author of this article and website, I very much enjoy reading and learning the opposing views of religion. Militant Atheist is just a generic term coined by Richard Dawkins, atheists in the slides above and in the article below, may not have agreed to that specific term. However their actions, surely signify they are set on a mission to defeat religion, and move mankind towards conquering our problems from within.
Sam Harris is near the top of the list of militant atheists. He has taken many many shots towards Islam, that he has hired a security team to protect himself. Which is an unfortunate reality of the world we live in. Harris, unlike many atheists, actually believes in Spirituality. He practices a form of buddhist meditation. Harris, sees the need for religion, but first, wants to remove the creator from religion.
Reasons for this are most likely pointed towards the moral factor of religion. In the Bible, for example, God told the Israelites to wipe out villages/cities in the Old Testament. In the Qu'ran, the tolerance for violence and revenge are Harris' deciding factors on why religion is immoral, and God needs to leave the picture.
If you can't prove it, it doesn't exist. Well that is Lawrence's motto with religion. Krauss will hold this view tightly in any debate, but when asked the opposite view of science. He claims that is the fun of it, figuring out what you don't know. Krauss is a very well spoken, intriguing debater, with a relentless oral attack that would make any inexperienced debater panic.
Krauss has written many books, including The Physics of Star Trek and A Universe from Nothing. Krauss was featured in a full-length film with Richard Dawkins in The Unbelievers. Where Dawkins and Krauss travel the world advocating for science and opposing religion.
Peter Singer is known for his stances on ethics, and uses morality to battle theism. Singer's biggest complaint about religion, is the suffering in the world. If there were a God, Peter may ask, 'Why does he allow suffering?'. Other factors that go into Singer's thinking, is the treatment of animals. In most religions, animals are soulless, and act as rather machines under god's creation. Peter takes the opposite view, and believes an animal's life is just as important as a human's. Peter's response to where morals should come from, is overall the betterment of a society.
Dennett is a facts based guy, and advocates for the world to teach children all the religions of the world. In his opinion, if children, see how religions evolved over time, they will clearly choose atheism. Dennett argues vigorously against creationists, and says natural selection is a universal acid that eats away at any creationist theory.
Carrier's biggest argument against religion, specifically Christianity, is that it's been done before. As an historian, he will cite many previous examples of resurrections, virgin births, gods that provide salvation, etc. Carrier does not point to a single major fallacy with Christianity, but relies on many minor problems that he sees, and when you add them all up, points towards Christianity being a false religion in his opinion.
Shermer enjoys poking fun at religion, as he promotes atheism/agnostic view points on his website, skeptic.com. One of Shermer's biggest arguments is that one's religious viewpoint is most often determined by their geographical location they were born and raised in. Unlike most of the other well-known atheists on this list, Shermer was saved during his young adult years, and even attended a Christian college.
As an Evolutionary Biologist, Dawkins attempts to slam religion on creationism. Dawkins believes religion is one of the greatest evils of the world. He frequently partners with Lawrence Krauss, in debates, movies, lectures, as they try to remove religion all together.