Why do atheists preach atheism? Well, I was an atheist for most of my life from about age six to nearly fifty - consciously, explicitly and publicly; so I know this from the inside in a way that many lifelong Christians obviously don't.
Atheists preach their beliefs because they regard this mortal life as the only real thing, and therefore they want this mortal life to be as pleasurable - and to have as little suffering - as possible.
Therefore, atheists regard religion as threatening, because (for atheists) religion says that untrue things outside this mortal life are more important than happiness or misery.
Every motivated atheists has some thing* that he regards as vitally-important to his own happiness and well-being, but which religion would interfere-with or prohibit.
And that (put simply) is why atheists preach their beliefs and argue against religion.
*That some thing could be almost anything in principle - but in the modern West is usually political (e.g. one of the leftist 'isms') and/or sexual... Because for many people sex is the second-most-powerful motivator after religion. So when religion is regarded as untrue, and deleted; then some aspect of sex/ sexuality tends, whether explicitly or covertly, to become the dominant motivator.