There are many definitions of atheism with regards to whether or not it is a belief system. Most say not. However a couple actually do say it is.
There aren't any standard definitions which define atheism as a belief system, (wikipedia and the free dictionary being nonstandard sources). Interestingly enough, you used part of the definition for 'atheism', ("doctrine"), and referenced _that_ term, instead of 'athesim' itself. Let's look at wikipedia's nonstandard definition of 'atheism' shall we?
"Atheism is, in a broad sense, the rejection of belief in the existence of deities. In a narrower sense, atheism is specifically the position that there are no deities. Most inclusively, atheism is simply the absence of belief that any deities exist. Atheism is contrasted with theism, which in its most general form is the belief that at least one deity exists."
The entry continues, (anyone can look it up), without defining atheism as a "belief system". Now, as to atheism being a "doctrine" we have:
1. a particular principle, position, or policy taught or advocated, as of a religion or government: Catholic doctrines; the Monroe Doctrine.
2. something that is taught; teachings collectively: religious doctrine.
3. a body or system of teachings relating to a particular subject: the doctrine of the Catholic Church."
Again, nothing about a "belief system" there.
So her opinion has merit to it in that there are some who consider atheism a belief system.
Alternatively, it appears from the reference sources that the word "doctrine" applies much more directly to religious beliefs than it does to a non-religious philosophy like atheism.
1.the doctrine or belief that there is no God.
2.disbelief in the existence of a supreme being or beings.
Oddly, that reference seems to define a 'disbelief' as a belief although the same source defines "disbelief" as:
1.the inability or refusal to believe or to accept something as true."
It takes just as much faith to believe in atheism as believers have faith in theism.
That does seem to be the a priori assumption in play however, applying "faith" to atheism is exxtremely specious. The reason being that theists declare that faith, (a lack of evidence), _required_ whereas atheism skeptically rejects a lack of evidence as a substantive basis and that doesn't require faith.
What's ironic is that atheists show they have strong faith in the inferiority of having faith.
Once again, no "faith" is required to be skeptical of a lack of evidence. Having "faith" in disbelief is not a logical concept.
This "faith" includes using everything in their power to influence others to join their atheistic "non belief."
Presumably, you are referring to the use of reason; something which most religionists abhor? You did include an inaccurate assumption in that atheism is not an evangelical organisation. There aren't any bicycle-rifing suits annoying suburban neighborhoods to 'spread teh atheist word'.
They also want to turn anyone and everyone away from the idea of any belief in God.
What the atheists I've met had in mind was to get people to actually use any inherent critical thinking ability which remains after religious indoctrinations to reason for themselves. They do this mainly by demonstrating some reasoning processes in the off chance that it'll catch on.
And in today's society, some have gone so far as to openly say that people who believe in God need to be "eradicated." All of this, in and of itself, shows that technically, atheism could be considered a belief system.
Fanatics can be found under many rocks; militant atheists would be no more surprising than militant 'onward xtian soldiers'. However, Falconeer02 indirectly requested a source for this - unless it was hearsay?