They don't need to disprove it just as I don't need to disprove the existence of the magic leprechaun. Its your responsibility to attempt to convince them that it exists, until then they can choose to abstain from believing in it, and at the same time, refuse to assert that it does not exist. That is if you are talking about agnostic atheists or "soft/weak" atheists. The real problem here is that people, especially religious people, confound the notion of a lack of belief with a belief in the negative of a claim; "atheists", and mostly inadvertently, add fuel to this problem by claiming both and by defining the later as a form of atheism (so called "hard atheism"). Im actually guilty of doing this in this very thread myself earlier.
The OT is actually right that people who make claims like "God (an all encompassing term) does NOT exist" not only have a burden of proof but the claim is indeed faith-like. The issue is that NOT ALL atheists or people who claim to be atheists make those sort of claims.
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Your claim about Darwin is also false. The theory of evolution as framed by Darwin himself and even as currently proposed has nothing to do with the origin of life. All it does is explain the origin of biological diversity. What you are alluding to is abiogenesis and you are right, that is more of a hypothesis than a scientific theory. Science can only "explain" things which are falsifiable and testable, it is inherently incapable of answering questions like "what is the meaning of life". More importantly, science does not need to explain anything. Religious people seem to have this idea that science's inability to explain some things implies the existence of God. Evolutionary theory could be falsified tomorrow (even if that has about as much chance of happening as atomic theory being falsified), it would not count as an iota of evidence for the existence of God.
As for "blaming" religious people, I personally don't care what other people believe insofar as it doesn't negatively affect me in some way.