Who says women didn’t matter? (Judges 9-10)

I’ve heard arguments before that the Bible is naturally chauvinistic because of the time period when it was written and that directives on husbands and wives and women in general should be disregarded because of the culture in which the text was written.  The passage in Judges 9 regarding the death of Abimelech is, to me, a reason why those other arguments should be tossed out the window.  I find it amusing that the very thing Abimelech didn’t want to have happen is actually what happened: records show that he was killed by a woman.  It was a shame and a disgrace to him that his life should be taken by a female, so he went through the necessary technicalities to have his armor-bearer run him through with a sword after a woman hit him on the head with a millstone.  So who actually killed this guy?  Since the Bible isn’t chauvinistic, it appears that a woman did.  Had the Bible been written by mere humans of the day, it would record that he was killed by his armor-bearer.  It’s a good thing we can believe all that the Bible has to say.