The vast majority of atheists and Christians alike, in my pretty considerable experience, hold their positions almost without regard to metaphysical truth. They hold them as the result of parental indoctrination, the pronouncements of supposed authority figures, or for cultural, social or economic reasons unrelated to metaphysical truth. Many would admit as much. Few can cogently defend or even explain their positions.
Atheists, as others have suggested, run the gamut from virulently anti-theist (and mostly mindless) New Atheists to extremely thoughtful and committed atheists to those who are more properly described as agnostics or seekers to those who have no clue what they even mean by the term atheist. Pretty much ditto for Christians.
I don't think any useful purpose is served by introducing a new term such as antitheist. Would it be useful to introduce a term such as whacked-out Bible-thumper? Any discussion has to occur at an individual level. For a meaningful dialogue to take place, the believer must understand what species of atheist he is dealing with, and vice-versa for the atheist. Identifying the species is seldom difficult.
For those who haven't read it, James Fowler's 1981 classic Stages of Faith is very instructive as to how all belief systems, including atheism, "work." Across the spectrum of all belief systems, the vast majority of adherents are forever stuck at one of the lower stages where reliance is placed on authority figures and no meaningful questions are asked or allowed. For a meaningful dialogue between an atheist and a believer to take place, both participants must at least be at Fowler's stage four.