Professing your faith =/= saying that someone else's belief is false.
Actually, yes - these are the mental gymnastics I can't stand.
I think you are confusing either what I'm saying or what you're saying. My statement is essentially definitional, not even really an opinion. There are multiple things that can be meant by professing one's faith, which can include not needing to comment on someone else's. It can also include
an opinion on someone else's without making definitive factual statements, and yes, of course it can also include declaring someone else to be objectively wrong. But the profession of faith can be made on many levels, not just intellectual, whereas a definitive statement of the falsity of someone else's claim does require a strong intellectual component. Not sure how you can say I'm doing mental gymnastics when professing faith is
literally not the same thing as just telling someone else they're wrong. And you are not even leaving out the potential for my profession of faith to include the possibility that you are are
partially right but missing important elements. Disagreement does not have to imply total negation, as you seem to imply.
But to proclaim yourself an atheist, means that you are also saying Christianity and every other theistic religion to be wrong. Same that if you say you believe in God, means that you're saying atheists are wrong.
I do not think this characterization is really representative of (a) most people who would call themselves 'atheist', and (b) not really meaningful in terms of assessing
what is wrong in the profession of a diverging faith/belief. For example one of the biggest cons in the anti-religion faction is that the dumb religious people believe in a bearded man in the sky. Where is the bearded man, they ask, show us with a telescope. I'm only being slightly cheeky in how I phrase this, because I think in many cases it's not far off. So for an atheist to say a religious person "is wrong" when what they are calling wrong is this idea, means they're not even talking about the same thing, no less contradicting each other. By contrast, a person of a particular faith, when confronted with an atheist, might well ask what it is they do believe, why they do, and what life experience contributes to this worldview. It's the totality of it that must be examined, along with the implicit metaphysics, etc (it doesn't have to be phrased like that, but that's what it entails actually). It is entirely possible, for instance, for a Catholic or Buddhist to have a fairly high degree of alignment of belief, even though obviously there cannot be a 1:1 mapping (or at least so Lewis claims, and which I agree with). So the issue isn't right vs wrong; that's a very narrow and actually misleading way to see it. While there are obviously ideas a religious person would tend to say 'are wrong', that is not equivalent to announcing a priori "anyone who disagrees with me is wrong". That's what theological/philosophical debate is about: to determine what, if anything, the disagreement actually consists in.
C.S. Lewis understands this plain fact. And so many others go into mental gymnastics to argue that when you say X is true, that doesn't mean you believe opposite-of-X to be false.
Yes, but the topic isn't just what the facts are, but rather our relationship to the facts. I didn't read the full doc that JoshuaD linked to, just the excerpt, but I've read plenty of other Lewis stuff, and I don't believe he would argue (or even accept remotely) that a religious belief consists of a series of truth-statements that can be listed as axioms, and these comprise the belief system as it exists in an actual human being's mind. Our thoughts are not a list of facts that can be written on paper, although obviously the formal logical apparatus comes into play to help. Socrates, I think, was acutely aware that the relationship between ideas, life practices, instincts, and even social awareness, have a very difficult to understand connection, and that you can't even really just say that X is someone's 'belief' and leave it at that. Not to change the topic and say we can't speak of beliefs in terms of fact, and Lewis does speak of fact, but be careful about strawmanning Lewis into saying things he isn't. I don't believe he would argue that the disagreement about facts such as he mentions in the quote can just be boiled down to some statements that logic can sort out neatly. In fact the Catholic belief, for instance, is that there are certain things our logic is not up to sorting out, and so there is a limit to how definite a claim one can make about these in certain regards, beyond certain basics. Ascertaining which sorts of things we can even be sure about, or which are subject to the weaknesses in our reason, is one branch of philosophy (and theology) that is non-trivial. So it's not just a "plain fact" as you suggest! That Lewis in a particular essay speaks of certain facts an atheist and believer wouldn't agree on, is to make a particular point: in this case I expect his point is to refute the "what's the point of religion anyhow, I can be a good person without it" argument, which is a popular one. He is most likely not making a statement about epistemology here, nor is he making a statement about what sorts of claims a Christian person makes as a profession of faith. For that you'd have to read a much longer work.
ETA - I should just mention I keep referencing Catholic ideas, despite Lewis having been Anglican, only because I don't really know much about Anglicanism compared to what I know about Catholicism. But on most of these topics I believe his intent was to communicate general
Christian truths, and not strictly sectarian dogmas.