'Arrogant' is an adjective meaning 'having or showing an exaggerated opinion of one's own importance, merit, ability, etc; conceited; overbearingly proud: an arrogant teacher ; an arrogant assumption '
It doesn't imply any defect in reasoning or lack of knowledge.
It's a perception of character.
It is better to be arrogant than ignorant.
As an alternative statement, I have no problem in ASSERTING my lack of belief. I suspect that part of theists' problems with atheists is that we present not just a different view, but one which is completely at odds with theirs, fact vs. myth, rationality vs. irrationality. The only real meeting of the minds that might be available is where they agree NOT to interfere with us or the government we live under. I've met SOME theists who will consent to that, but they are remarkably RARE.
I suspect the "arrogance" they perceive is more in the radical departure from their mindset, as well as the rejection of the hierarchy mark d mentioned elsewhere ... and I don't see that it can be helped so long as they wish to continue to indulge in their hallucination.
They think it is arrogant because to accept that there is one
"proves" that you are humble enough to admit that there is someone who created you, the world, and everything else. It "proves" that you are nothing more than God's ...whatever and that you are not the master of your own life.
And to say you do not believe, goes against their very stringent rules one and two. Basically if you believe in God, you are more likely to be humble..they think...(but I disagree)
The other day, I related a story about another Christian doctor to my new Hindi doctor. The Christian doctor said something incredibly heartless and vicious to me which I relayed to my new Hindi doctor. He had a lot to say (mostly under his breath) about the arrogance of Christians. To a Hindi, the belief in only one god and forcing that one god down the throats of everyone else is arrogant.
To other religions, the Christian assumption they are always right about all things spiritual and all other ways are wrong is arrogant.
I always tell my other than christian acquaintances that I am an atheist and I do not believe in their faith (which they are used to living in the US), however, I do not believe their faith, beliefs are invalid or in any way less than any other. I usually get along with them pretty well. They may tease me about my lack of faith, but usually they are pretty happy to be around someone a lot less arrogant and judgmental than most christians are.
What the atheist says: "I do not believe the assertion that any god or gods exist."
What the theist hears: "Your belief in a god is stupid."
"Your belief in a god is stupid."
I didn't know that christians had ESP!