Antony's first in-depth comment sets the tone:
Because the question has been settled to my satisfaction. I say “there is no God” with the same confidence I say “there are no ghosts” or “there is no magic.” The main issue is supernaturalism — I deny that there are beings or phenomena outside the scope of natural law.That second paragraph is important. Antony is rejecting gods of the gaps, while rejecting scientism at the same time. In short, this is not going to be a defense of atheism like Sam Harris might offer.
That’s not to say that I think everything is within the scope of human knowledge. Surely there are things not dreamt of in our philosophy, not to mention in our science – but that fact is not a reason to believe in supernatural beings.
Indeed, Antony rejects interviewer Gary Gutting's idea that religious belief might be a hallmark of irrationality (let alone the mental illness canard) with this: "I’m puzzled why you are puzzled how rational people could disagree about the existence of God."
More on that is near the end of the interview:
It is disrespectful, moreover, to insist that someone else’s belief has some hidden psychological cause, rather than a justifying reason, behind it. ...Well put. And, that holds true even if a certain strand of the religious refuses to engage in such courtesies.
I believe I have reasons for my position, and I expect that theists believe they have reasons for theirs. Let’s agree to pay each other the courtesy of attending to the particulars.
Antony later extends that courtesy to religious beliefs in the public sphere:
No one needs to defend their religious beliefs to me — not unless they think that those beliefs are essential to the defense of the policy they are advocating. If the only argument for a policy is that Catholic doctrine says it’s bad, why should a policy that applies to everyone reflect that particular doctrine? ...She then cites drone warfare as a particular example
But usually, religious people who become politically active think that there are good moral reasons independent of religious doctrine, reasons that ought to persuade any person of conscience.
Antony then goes to note, per the old atheist trope that we just believe in one less god than Christians, Muslims or whomever, who are atheists in terms of Zeus, Thor, etc., that rational people within the large set of religious believers disagree among themselves.
She makes this important point, about that diversity:
I’m challenging the idea that there’s one fundamental view here.From there, Antony rejects the idea of epistemic peers. She doesn't claim that all knowledge is subjective, or that their are individualized facts. She does, though, note that we all bring our individual past perspectives to the table.
Antony then addresses what many people call "spiritual" experiences. I do not, because the term eventually gets twisted. Antony talks about "profound" experiences that, for her, did not become conversion experiences:
I’ll admit that I believe I know what sort of experiences the theists are talking about, that I’ve had such experiences, but that I don’t think they have the content the theists assign to them. I’ve certainly had experiences I would call “profound.” Many were aesthetic in nature — music moves me tremendously, and so does nature. I’ve been tremendously moved by demonstrations of personal courage (not mine!), generosity, sympathy. I’ve had profound experiences of solidarity, when I feel I’m really together with other people working for some common goal. These are very exhilarating and inspiring experiences, but they are very clearly about human beings — human beings at their best.That's the bottom line, and how Antony is a good humanist as well as good atheist.