Ok now that I’ve stopped dancing and listened to it, I can share one experience similar to what you mentioned:
I was approached by two Jehovah’s Witnesses in a coffee shop, because one of them noticed that I was reading a book titled “Does God Exist?” The conversation quickly turned to eschatology and even after I tried to push things toward John 17, and as a result realized that these folks were pretty good at what they did. So I went and quickly Googled “Responding to JW’s” and found some quick arguments in order to make any future encounters more favorable to my position and less likely to continue on to eschatology.
I imagine many atheists are in the same boat. They buy that Dawkins book because they’ve experienced a Christian evangelist in an uncomfortable situation that has pushed them to find some “quick arguments”. Except for the atheist I think the thing they want to avoid is the personal challenge of the gospel instead of eschatology.
Anyways, that situation definitely made me realize how others may perceive and respond to Christianity, and perhaps a clue as to why New Atheism has caught on the way it has.