Blackford's essay takes it's title from that moment in our lives that many of us are familiar with: that point at which we decide that religion has become, for us, unbelievable. This moment is not exclusive to religion, of course. We have similar moments with Santa, the Tooth Fairy, or the Easter Bunny, but religion seems to be a little different. Unless you were lucky, it's a good bet that you had to work it out for yourself that religion was Not True. For me, I remember sitting in the pew sometime in my early teens as my moment of unbelievability. I don't remember the exact sermon, but I remember it all coming together in a rush. Well, maybe not *all*, but enough.
For Russell, the big kahuna is the problem of EVIL (bwahahahaha.) This has traditionally been, and largely remains, a problem for believers in any traditional sort of theistic deity. This deity is forced to have an unimpressive amount of knowledge or control, or to be in possession of a most impressive bad attitude. There really is no other option, I'm afraid. The resulting fallback position of invoking "mysterious ways" has come to have a distinct "scraping the bottom of the barrel" ring to it. And if there is anything new about the New Atheism, it is in it's willingness to press this very point: believers do not have good reasons to believe what they say they believe.
Russell ends his essay with a call to arms, of a sort, for nonbelievers: openly challenge the undeserved respect that religion enjoys. Stand up and ask hard questions. Make your voice heard as a member of the growing number of reasonable and rational people that find the claims of religion to be unbelievable.