Whilst it may be technically correct to say that atheism is a rejection of belief rather than a belief in itself, isn't it true that in order to lack belief in God you must have certain other beliefs? Such as: the world was created via natural processes, there is no such thing as inherent good or evil, the bible is fictitious. By attempting to convince somebody to become an atheist, as this book encourages, I consider it quite reasonable that it is trying to convince people to hold actual beliefs. Therefore I continue to consider the term 'athest evangilist' completely valid.
You might consider it valid, but that doesn't mean it's actually so.
For example, the statement "the world was created via natural processes" is not inconsistent with the statement, "gods exist". It might be inconsistent with "the god of the Bible exists", but that is just one god out of the innumerable gods proposed by humans. For example, what if gods were also created by natural processes, for the sake of argument? Or what if those natural processes were set in motion by a god, but that god didn't create the world?
It's true that the author of that book doesn't accept that gods exist. But the actual belief, or worldview, that he's proposing is one based on reason and rationality. That is to say, that we should base our beliefs on what we can demonstrate through evidence, rather than superstition. Through reason, rather than faith.
If you want to argue that he's evangelizing for reason and rationality, I'd have no quibbles with that. But there is no reason to assume that an atheist must be reasonable or rational. Indeed, the existence of atheist 'churches' suggests that some atheists may very well not be as reasonable and rational as others. Therefore, you should probably rethink your argument.
By the way, all that being synonymous means is that two words share a meaning. It does not mean that those two words always mean the same thing. For example, teaching is a synonym of evangelizing (according to the thesaurus Mr. Blackwell linked). Does that mean that the two words are always going to be synonyms? Of course not! That's why it's important to use the word you mean, and not rely on something that's merely synonymous.
Once, when I was quite a bit younger, I referred to someone as being ossified. My brother didn't know what the word meant, so I clarified by saying it was like something that was petrified. Then he asked me, if I'd meant petrified, why didn't I just use it in the first place? Well, the reason is because I meant ossified. Ossify and petrify both refer to the process of something hardening - but only ossify refers to the hardening of attitudes. When you refer to someone being petrified, it usually means that they're afraid.
