I agree with this. The only thing a theist actually has is faith, nothing else. There is no evidence of or reason to believe in a god. It is purely faith based.
But it is incorrect to say then that all things are faith based. As science does produce good evidence as well as good reasoning for holding a position. As well most people base their life on experience and what has worked for them in the past. Where as a belief in a god is personal and nothing more than faith holds it together as there is no past experience of a god.
You demonstrate well the problem with the theist thinking. That your beliefs are faith based but even so you still attempt to use reason to establish some cause for having faith. In this case a false reasoning that if believing in a god is faith based then everything must be faith based.
You are also incorrect about atheism. It is not an attempt to prove anything. It merely points out the fallacious thinking of a theist. It points out that whatever evidence a theist believes in is not in fact evidence of any such thing. You have forgotten that it is up to a theist to produce evidence or reason and not the job of an atheist to create and then disprove evidence or reason.
Science is not evidence. Neither does it produce evidence. Science is a set of falsifiable theories. This definition of science comes out of the reasoning by Karl Popper. By rejecting the use of supporting evidence for a theory, the only remaining test is the null hypothesis, that is, how can you test the theory to see if it's wrong?
No theory of science is ever proven true. A theory remains a theory until it destroyed by falsification. The reason theories of science have a stronger case than any other kind of theory is the test of falsifiability.
Science itself cannot prove whether a god or gods exist or not. Neither can logic. Both are atheistic. Neither address the question, because the question is not falsifiable for either case. Logic is a closed system, much like mathematics. It operates only in that closed system. The question of the existence of a god or gods existing or not cannot be answered by logic either. It's like trying to prove such a thing with mathematics.
This doesn't mean science rejects the idea of a god or gods. It simply doesn't go there. This is atheism...not a declaration that a god or gods do not exist, but that the question is simply irrelevant. Both science and atheism do allow for the possibility that a god or gods MIGHT exist, but don't try to prove one way or the other. It's simply an irrelevant question.
This is hopefully close to how you approach atheism. It simply doesn't address or believe that a god or gods exist, yet it does allow for the possibility of it.
This is different from an agnostic. An agnostic believes a god or gods probably exist, but refuses to ascribe a nature to it. The agnostic simply says a god or gods probably exist, but stops there and goes no further. Similar, yet different.
Then there is the 'militant' atheist. This is the kind that tries to prove no god or gods exist, despite no way of doing so. This is actually a religion, as it is based on an initial circular argument like any religion. It points to supporting evidence like any religion. It builds model after model upon the initial circular argument like any religion. This is a much different kind of atheist than you are describing yourself to be. They do exist, however. Their position is a fundamentalist one...arguing by repetition, insulting any that dare oppose them, and generally 'condemning to hell' any that does not see their view. It is this individual that builds the image of atheism as a religion. For the 'militant' atheist, it is.
I do not think of you as the 'militant' style of atheist. Your arguments are following well reasoned patterns. You seem to be one of the few atheists that do not try to prove one way or the other. Be proud of it. It means you have learned to think for yourself...a rare commodity these days.