I haven't heard them argue that they want to use "Atheism symbols" instead. They just don't want state-sponsored religious symbols, particularly when those symbols are Christian, because so many people believe that Christianity is our national religion which is bullshit. Also, American Atheists don't give a damn about stuff that is on private property, only stuff that is owned by the government on government soil. That is, in essence, state sponsored religion, which IMO is unconstitutional. IANAL though.
The "last sentence" was not part of a purportedly cited source, it was merely your opinion on the arguments that atheists in general are making. Cite me a source where American Atheists are saying that they want "Atheist symbols" used in place of crosses and I'll concede the point, but I don't think that has happened.
As a side note, what would be considered Atheist symbols anyway? Atheists do not believe in any given God. I guess you could argue that the big fish eating the little fish are Darwinian symbols, or the FSM symbol is one that many Atheists use to mock religion, but Atheists in general do not have a symbol.
Doesn't really change the facts. American Atheists are not arguing that they should use Atheist symbols. The article you used just says "some atheists" are making that argument, with no citation, examples, or any sort of fact behind that.