Tec - everyone is an atheist in some form or another (most would have cogent and rational reasons for not being convinced of the reality of Zeus) however, when it comes to dismissing and disproving gods it is, in my limited experience, those who wish to posit another supernatural cause that spend most time and effort fighting specific gods and proving their targeted atheism (ref JW pages of literature disproving Catholics etc.) whereas atheists (the broad term I'm applying to those who acknowledge no deity due to lack of convincing evidence) tend not to care very much about god x or god y but rather see all forms of religious faith as stemming from equally understandable (and logically wrong) reasons and arguments against gods being broadly equal (that which proves Jehovah could be said of Zeus and that which disproves Zeus would tend to be a problem also with Jehovah.) I am no longer particularly bothered by mormon Elohim for example but I also absolutely understand a JW's committment to Jehovah.
Atheism itself is a rather healthy starting point being the natural state of children and alone is a laudable position imo. Once a person has decided to be an atheist with the exception of one deity or pantheon of grouped deities then they have very much narrowed the field and will begin to have a very active mindset in finding , often small, differences between their 'real' god and the pretend ones and explaining how important that is in proving the veracity of their god and the impossibility of everyone else's. If all people could believe in their various god's with a very healthy dose of skepticism and doubt it would be a brilliant start to gleaning truth and value from various creeds but sadly most gods are jealous and like to future punish non-believers while preparing a really awful place for those half in and half out the faith (some actually 'spew them out').