Jimmy Snyder said:
Only a pedant would say that an atheist is an agnostic. The etymology might be on your side, but the meaning of the word abandons you. I have never heard anyone say "I don't believe in G-d" except to mean "I believe no G-d exists". It's like "I don't believe in the Easter Bunny". Who ever says "I believe the Easter Bunny doesn't exist"?
Maybe this will provide some context why some people will say they're a "weak atheist" rather than "strong atheist", or lack of belief rather than believing there are no gods:
If someone asked you what you think about the Easter Bunny, you'd probably say, "I believe there is no Easter Bunny." However, if someone asked what you think about aliens or UFOs, many are going to say, "I don't believe in aliens." However, probed they'll admit they don't actually deny that aliens or even UFOs could exist, but rather they just plain don't believe. If you then say, "Okay, so you're agnostic toward aliens/UFOs," they may get upset because they think you're taking them out of context, because it's like you're calling them a fense sitter when they just don't believe. (Many who are heated into the debate about gods will accuse agnostics of being fense sitters who can't make up their minds, so some who don't believe in any gods just prefer the word "atheism", even if they don't deny the existence of any gods).
Another way to look at it, there are many Catholics and Jews who say they do actually believe in a God of the Bible, but that their belief isn't that strong. If you probe and ask if the Hindu gods may possibly be true, some may perhaps say they don't deny any of them, but they just don't believe in them. If you call them agostic toward Hindu gods they'll then think you're taking them out of context. The same for some who practice Hinduism, they'll think the same way if you accuse them of being agnostic toward the God of the Bible (although just to add in there that there are some denominations of Hinduism who think the God of the Bible is just another manifestation of their god, although not all denominations necessarily believe that).
So I think that's why they say there is weak atheism vs. strong atheism, "not believing but not denying" vs. "actually denying there are any gods".