Historically, most societies are strongly to totally male-dominated. I know many societies had occasional female rulers (Catherine the Great, Elizabeth I, Mary, etc), but even then they were exceptions and virtually everyone under them was male. At what point did it become regular for women to have equal authority in ruling a country?
Side question. I read in wiki that in Catalhoyuk there's no evidence of sex being relevant for social status, and that this is a common feature of paleolithic societies. Is this accurate? If so, what is the first society that we know about in which there's social distinctions based on sex?
This is a really problematic question, because there's no real definition for a truly equal society. Is femaly suffrage enough? Some kind of law prohibiting discrimination of any kind based on gender? Actual enforcement of those laws and enough women in important roles in society? A completely gender-neutral world where all statistics are equal to both genders? I don't want to get pedantic here, but a lot of people would say that there are even now no societies that fit your description.
If you think that the modern day USA and Europe are equal enough for the purposes of this question, then the answer would probably be one of the Nordic countries. Saying "probably" not because I feel I don't have the knowledge to answer this question, but because one can't give a specific answer to a vague question.
There are a number tribal societies that have survived in the hunter-gatherer lifestyle, which are claimed to be completely gender-neutral, and I imagine some of them actually are. If this is true, then there have certainly been countless such pre-urban societies before recorded history and finding the first amongst them would be completely impossible.