The issue isn't whether it's objectively convincing but whether it convinces enough people who matter, unfortunately.
Look at what has happened to (educated) public discourse over the last ten years or so. It's gone from classic liberalism to something else entirely.
The liberal approach which we probably all grew up with was that it's the contents of an argument that counts and the characteristics of who makes it are irrelevant, except that a person's background might their argument more informed (but the proof of this would be in the argument itself.) This view was left of conservatism, which was more 'don't rock the boat'.
Now we have the a different approach, ie, that you have no standing to comment unless you have the right, ie minority characteristics - which Dawkins doesn't have. Because this reasoning applies to social issues - which aren't easily resolved by science - Dawkins' undeniable eminence counts for little. What matters is that he's a stale pale male.
It's a sharp leftwards shift - and that's why Dawkins and co look like right-wingers now. They've been left behind. I say it's a leftwards shift because it has its origins in thinkers influenced by Marx. It's also very hard to argue against because it's an internally consistent theory that functions without much need for evidence. Someone - it might have been Arabella - posted a link to an article by Slavoj Žižek a couple of weeks ago. It was all very erudite on the surface but...