>

This is why he wanted to define them. The commenter presented the "logical and epistemological" definitions of the words, not the colloquial uses of the words.
I think that it all revolves into a definition problem. 
Just to be sure, could you define the terms you're using ? 
Personally, those are mine: 

Theist: I believe in God(s)
Atheist: I do not believe in God(s)
Anti-theist: I believe there is no God(s)

Then there is the "knowledge" axis: 

Gnostic: I got evidence about my belief
Agnostic: I got no - evidence for my belief

Also, you need to define if you are a giving a general sentence (i.e. I'm anti-theist for all Gods definitions), or just about the specific Christian definition (i.e. I don't believe that a celestial immortal magician created the world in 7 days and hate human masturbation). 
Because if you think that anti-theism make more sense whatever the definition of God (and not only the Christian one), there are plenty of cases where atheism make more sense:
Why couldn't we live in a simulation created by a higher specie (for example, imagine we're currently some really intelligent NPC in a "the sims" game for more advanced society) ? In that case, there are Gods: the guys who developed the simulation. They just don't interact with humans because that would skew the simulation. Such a situation is not totally improbable, as the only intelligent specie we know (us) currently create simulations that are getting smarter and more impressive with years. So being an agnostic atheist (in the sense that we don't believe because we have no proof in both direction) seems to be the most sensible choice when we talk about all the possible definitions of gods. >

You’re anti-theist definition is wrong. It’s the position that theism is should be opposed. 
That’s the case he’s making and the case is strong.