also the chart is just flat out wrong. Atheism is just a lack of belief in a god. Answering "I don't know" means you lack a belief in a god, making you an atheist. It just makes you an agnostic atheist. Answering "No" would make you a gnostic atheist.
I would just say that there's no perfect agreed upon definition/clarification for the words Atheism and Agnosticism.
Your approach, that of agnosticism being a subset of atheism is one view I've seen, mostly on this website.
However, the curriculum of my A Level Religious Studies course had a different view. That being that;
- Agnosticism is a choice to neither believe there is or isn't a God/gods. It accepts that there could be a deity and therefore isn't atheism.
- Atheism is the act of not believing in a God/gods. It can be further divided into two forms;
-- Hard Atheism: A chosen disbelief in deities, often stemming from personal consideration on the matter.
-- Soft Atheism: An unchosen disbelief in deities arising from having never considered the existence of deities.
So for me, I identify as an Agnostic, but not an Atheist. While I don't believe there is a God, I also don't believe there isn't a God. I don't know if there is or isn't a God. And I believe it would be foolish to take one view over the other without more concrete evidence.
You might label me as an agnostic atheist, but to me the title of atheist implies that I won't consider the possibility of a God.