@TheLordOfLight I get what you're saying and I used to think that myself for a time. But then I decided to look up some defintions to be able to correctly identify myself and people I encounter.
What you're reffering to is a specific subdevision of atheism called "strong atheism" There are many different types. In the general sense of the word, the disbelief in the positive claim does NOT imply belief in its negation. It's a thing that a lot of people confuse.
Here's the Wikipedia definiton of Atheism in the broader sense and then more specific types of it.
en.wikipedia.org/wiki/Atheism "Atheism is, in the broadest sense, the absence of belief in the existence of deities. Less broadly, atheism is the rejection of belief that any deities exist. In an even narrower sense, atheism is specifically the position that there are no deities."
Another example are implicit atheists who simply haven't learned enough on the topic, let alone be in a position to believe either positive or negative claims.
http://www.humanreligions.info/types_of_atheism.html"Implicit atheist (lower case atheism) is a person who has not yet learned about god(s), theism or religion. All people are born implicit atheists."
"Strong atheist and positive atheist are both words for a gnostic atheist, although not all gnostic atheists are completely sure that gods don't exist - many are only quite sure."
"Weak atheists are agnostic atheists. They lack belief in gods, but don't think it is sensible to say that gods definitely can't exist."
So in essence, what you're saying applies to some atheists but you can't simply assume the person you're talking to affirms the negative proposition just because they identified themselves as atheists. You have to ask specifically. Of course you could just ask each person to describe their position cause not many have looked that deep into definitions. But the misconceptions about what atheism is are so widespread that by far the most people you'll encounter will just go on to assume your beliefs right after you say you're an atheist and you can't have an honest discussion like that. So I clear it up whenever I can.