Answer:
The superiority of the broad over the narrow definition lies in the fact that it allows us to describe a wider range of positions. The broad definition of atheism is thus superior because it helps us take into account a greater diversity of positions among real people than a narrow definition of atheism will allow.
For those who insist on the narrow definition, there are three basic positions:
- Theism: belief in (my) God.
- Agnosticism: don't know if any gods exist.
- Atheism: denial of (my) God.
Once we introduce the broad definition and recognize that agnosticism is about knowledge rather than belief (a related, but separate issue), we find that there are now four categories available:
- Agnostic Theism: belief in a god without claiming to know for sure that the god exists.
- Gnostic Theism: belief in a god while being certain that this god exists.
- Agnostic Atheism: disbelief in gods without claiming to know for sure that none exist.
- Gnostic Atheism: disbelief in gods while being certain that none (can or do) exist.
It's true that human beliefs are complex and both of the above two systems are simplifications, but the latter system not only recognizes more points on the continuum of human belief but also makes room for grey areas because they introduce the question of how certain a person might be.
The broad definition of atheism is also superior for the simple fact that it is more reflective of reality than the narrow definition of atheism is.
When you come right down to it, we can't ignore the fact that there are people who do believe in some sort of "god" without claiming to know for sure one exists and there are people who don't believe in any such thing without claiming to know for sure than none can or do exist.
Both of these groups share in common a refusal to claim to know for sure that some god does or does not exist, which justifies calling them all agnostics — but if the former are agnostic theists, then what can the latter be if not agnostic atheists?
No debate over the definition of atheism can pretend that such people don't exist. Not only do they exist, but their position is distinct enough from agnostic theism to justify differentiation. Using words like "nontheist" does not help.
There is no sound, valid argument to not apply the "atheist" label to them.