Something cannot be what it is not. Nothing is defined by what it is not. When you say, “Atheism is the lack of a belief,” you’ve done it, right there.
Atheism is (atheism being something) the lack of a belief (the lack of anything is nothing). You’re right in saying that atheism lacks belief, but not about what atheism is, only what it lacks. I you use the definition “the lack of”, you’re saying something is what it is not.
“Something cannot be what it is not. Nothing is defined by what it is not.”
I disagree on this point.
If it is normally expected that something should have a property and it doesn’t, then it is perfectly fine to define it as what it is not.
For example, if gas normally has lead in it and you have created a type of gas that doesn’t have lead, it is perfectly fine to define it as: unleaded (“gas that does not have lead”).
And if people are normally theists (90% in America) and you are not, then it is perfectly fine to define yourself as: atheist (“not a theist”).
So what makes atheists unusual is precisely that they don’t have a property that most people throughout history have had: belief in God. Defining them that way distinguishes them. It says “we know most people feel they need this property, but we don’t feel that way, so we don’t have it.”
If it ever becomes the case that most people in the world are atheists, then the term “atheist” will become meaningless because there will be no sizable percentage of theists to contrast them with.
Here are other examples of things that are defined by what they are not:
In other words, if, in a particular context, something is expected to have a property and it doesn’t, then it is noteworthy to point out that it doesn’t have that property.
People in the modern world, especially America, are generally expected to have the property of “belief in God”, so if someone doesn’t have it, then it is noteworthy to point out their lack of that property.
So I am an:
atheistic human (or “atheist” for short)