This is pure semantic sophistry.
An atheist says: I do not believe in -god-.
Therefore: it is a denial of something which is defined as existing. By not believing in what believers believe.
Personally the definition of -free thinker- might be more appropriate. Nothing to deny for starters.
"accept the idea of god." Well, let me think about that. I accept the idea of Athena, Diana, and The Triple Goddesses; they all are "Wisdom Goddesses." Now, where does that leave me?
The ancient pagan gods and goddesses are no better at empowering me to think critically than YHWH, Frigg, Jupiter, Zeus, Nuit, the christian god, Allah, Apollo, Helios, or Ra.
If I have a broken leg, none of these god/goddesses help me, except, perhaps, help me retain my calm as I go to the doctor.
If I sit with a dying son, I am not comforted by promises any religions offer me.
If I observe my great-grandchild struggling with an illness, the resource I seek comes from science, not faith.
If I believe in god - any god - my tomatoes do not grow more productively. I am able and willing to learn how to prepare the soil for tomato seeds that I start in April and set outside in June that give me what I want and need.
Putting my belief in something by faith offers little satisfactory consequences and comfort.
Comfort comes from those around me who love me and whom I love. They are necessary and sufficient to meet my longing. A community does not just happen. It requires time and effort and commitment.
To me, "free-thinker" exists as another word for atheist. Personally, I refer to myself as an atheist because "Atheism is not an affirmative belief that there is no god nor does it answer any other question about what a person believes. It is simply a rejection of the assertion that there are gods. Atheism is too often defined incorrectly as a belief system. To be clear: Atheism is not a disbelief in gods or a denial of gods; it is a lack of belief in gods."
~ American Atheist,