Atheism is anti-religion and atheists want to ban religion from society.
Atheists often criticize religion, so a perception develops that atheism must be anti-religious but this is not quite true. Atheism is just the absence of beliefs in gods and can thus occur inside or outside the context of religion. Thus, an atheist might be devoutly religious, devoutly anti-religious, or completely apathetic with regards to religion exactly as with theists. It all depends on the individual and what ideas, beliefs, or principles they have aside from atheism.
This particular myth is often used to depict atheists as inveterate and irredeemable enemies of religious theists. For this reason, it's helpful to keep in mind the fact that it's not uncommon for theists, including some religious theists, to criticize and even bash religion themselves. There are for example people who consider themselves "spiritual," and even though spirituality isn't actually distinct from religion, they believe it is and that spirituality is "good" while organized religion is "bad" (such as intolerance, rigidity, and materialism). There are many liberal religious believers who criticize conservative and fundamentalist religion. There are conservative and fundamentalist Christians who argue that their beliefs are a "personal relationship with Jesus Christ" and not really a religion.
So does this mean that theism is anti-religion and theists are characterized by an absence of religious beliefs? Of course not. What it does mean is that there is no necessary or inherent correlation between theism and religion, or being a theist and being pro-religion. Although most theists are religious, with theism being part of a web of religious beliefs, some theists are not religious and their theism is part of a web of non-religious beliefs. Just because you are a theist doesn't mean that you have anything good to say about religion, religious beliefs, religious institutions, religious traditions, etc.
By the same token, just because many atheists criticize or attack religion, that doesn't mean that there is a necessary or inherent correlation between atheism and being irreligious or anti-religious. Although most atheists (at least in the West) may be irreligious, many atheists are religious and for some, their atheism is part of some religious system. Here is a partial list of some religions which are explicitly atheistic (rejection of gods is openly promoted), implicitly atheistic (gods play no role, positively or negatively), or which come in atheistic as well as theistic forms:
- Religious Humanism
- Ethical Culture
If all atheists are anti-religion and want to ban religion, then the atheistic adherents of these religions would have to be opposed to their own religion want to ban it. Does that make sense? Of course not. Therefore, the claim about atheists being necessarily anti-religion has to be mistaken.
If it isn't necessary for atheists to attack religion, why do they do so? There are as many different answers to that as there are to the question of why some theists attack religion. Religion has not been an unmitigated good for the world and humanity. Quite a lot that has gone wrong can be traced back to religious beliefs, religious attitudes, and religious power. This is not to say that there has never been anything good about religion it also hasn't been an unmitigated evil, either but there are many historical, cultural, and philosophical reasons which can justify criticism of religion.
We can add to this many personal reasons why someone, whether atheist or theist, would criticize religion: bad religious experiences when growing up, bad religious experiences currently, and a sense of unease over the involvement of religion in problems occurring today. Thus, there are atheists who do hate religion and a few who might ban religion if given the chance. Theists who are critical of religion see all of this, too, and there are hardly any atheistic critiques of religion which could not in theory be made by some theists.
If that's the case, then, why do most of the very pointed criticisms of religion come from atheists rather than theists? The answer is probably the same reason why atheistic religions are more common in the East than the West and anti-religious atheism is more common in the West than in the East. In the West, atheism and atheistic groups have been a primary locus for freethought and dissent from religious authority and religious institutions specifically Christian authority and Christian institutions.
Christian theism has dominated Western culture, politics, and society for over 1,500 years and there have been few sources of religious or theistic resistance to this domination. This means that most people engaging in such resistance have ended up being pulled into the sphere of irreligious atheism rather than into an alternative and theistic religious system. Atheism doesn't have to be irreligious nor does it have to be anti-religious, but cultural trends in the West have caused atheism, irreligion, and opposition to religion to be drawn together in such a way that there is now a high correlation among them.
This correlation doesn't change the fact, though, that it's a myth to regard atheism itself as inherently anti-religion, no matter how many atheists you encounter also happen to strong critics of religion. You can't assume that all atheists are opposed to all religion or that all theists are in favor of all religion. Such correlations are common, but there are too many out there who don't fit this pattern to justify gross generalizations and hasty assumptions. If you want to know what a person thinks about religion and religious beliefs, you have to ask them and you have to consider their response for what it actually says instead of imposing preconceptions you may have developed over time.