I'm not only prepared to acknowledge it; I'm prepared to show it to you:
War.JPG
Ares says there are some things only a god can teach. I absolutely acknowledge that he says this, and that it seems like reasonably credible claim. But he does not say that he's the only god that can teach these things, and he doesn't say whether or not there are also some things that an Amazon can teach that a god, or at least he, cannot. Logically, "X can teach something Y cannot" does not entail ""x can teach everything Y can." As an ilustration of this logical principle, consider this: Muhammed Ali may have been a better fighter--and potentially a better boxing instructor--than my local karate instructor, but that doesn't necessarily mean that Muhammed Ali could teach karate.
Does it seem likely that the Amazons know something about war that the god of war does not? No, it doesn't--but the text doesn't say, one way or another. Does it seem likely that the Amazons can teach something Ares cannot? Reasonably likely, yes. Though he has a lot to teach, Ares is not depicted as a very effective teacher. Just imagine this on your next performance evaluation: "Brettc1 is amazingly knowledgeable about science, and he knows some things about science that none of our other science teachers know. He also taught an excellent lesson about not harming one's lab partners (though this lesson was accidental, as he was attempting to teach the opposite). However, two incidents in a thirteen-session course raise some concerns about his class management skills: he almost killed a student, and he tried to induce that student to murder."
One has to ask: If Ares had been Diana's only teacher, would she have lived to the age of 12?