For one thing, how do you differentiate such differences? How do you determine if one family was of a higher class than the others? How do you determine if a society was matriarchal?

Answer: You have to look at the archaeological materials left behind. We have nobody to ask or observe. So, to determine if social class was a factor in a prehistoric society, we have to examine the artifacts. If there is a noticeable difference between artifacts, if much nicer artifacts or luxury goods are being concentrated with one small subgroup of people, then you have class distinction. If everyone uses the same types of artifacts, and everyone uses the same materials, and there are no distinctively status-defining objects left in the material record, the only conclusion is that any social status was not marked by objects or a difference in personal property. Thus, people all used the same materials of the same quality, and did not observably differentiate themselves into classes. This is the definition of an egalitarian society. Of course they may have had a specific person or group of people who made decisions, but that is not the same as an "egalitarian" society, by archaeological definition. There were probably certain people who had situational leadership, who made decisions, but who did not differentiate themselves into a higher class based on material culture. That's how we make that difference.

I can't comment much on matriarchality, that's not something I have studied in any detail. Just as it's difficult to study class divisions based on objects, it's even more difficult to study gender divisions. In my limited understanding, most of the Matriarchality scholarship came out of feminist movements in anthropology, and was proposed as an alternative theory which, at the time, did not have much evidence against it. We now have significantly more evidence, and the evidence is much more towards the idea that women were not power-holders in a political sense.

There were a lot of fertility figurines, objects with breasts, and this influenced many early anthropologists to think that fertility goddesses were the main objects of worship and therefore females were thought of has having more power. However, many of these objects can also be considered to be phallic in nature, with the two lumps being testicles as well as breasts, depending on whether you held the object vertically or horizontally.

I am sure life was not "idyllic" for early people, but we have to go where the evidence leads us, and for prehistory, where there is no writing, does not leave us much evidence to go on. We struggle with more esoteric aspects of society, such as ideas and religion and beliefs, because, unless they are explicitly laid out in the artifacts, we can't see it. This is the main principle behind Hawkes' Ladder of Inference. Basically, the more esoteric the idea or aspect, the less likely archaeology will be able to address it without writing. Social/Political insititutions and religious beliefs are the two highest rungs on the ladder, and thus the most difficult to understand. Thus, many, many different theories are created based on the evidence at hand, combined with anthropological theory about how people work, and results in any number of models for how prehistoric society worked.

The reality in the ground is: a limited number of artifacts, no differentiation in quality of artifacts, no evidence of class distinction, therefore an egalitarian society of hunter-gatherers.

EDIT: attempted to correct potentially confusing definitions

For definitions on societal divisions, please check out: The Archaeology of Rank by Richard Ames.

This may be a question more suited for /r/AskAnthropology, since you're asking about a time period where there is no written historical record or account.

The roots of this kind of thinking are very deep, and although classical authors already fantasised about a feminine, pacifist (and whatever) past, in modern times it can be traced to Rousseau's idea of the noble savage. The idea of the Romantic movement, as opposed to the Enlightenment, was that humanity 'by nature' was gentle, feminine etc. This idea also inspired for example the paintings of Rosetti, Alma-Tadema, Millais etc, basically all the characters that we still associate with Victorian classicism. In this milieu also arose archaeology, as well as academic history. Early archaeology, when it made expeditions into the Mediterranean, did try to find this ideal society, and the great finds of the period, such as Evans on Knossos, or Stephens and Catherwood on the Mayans, they did persistently present their finds in support of the romantic past. While Crete and the Mayans have shed this image since the '70s, it was primarily the quite rudimentary investigations at Malta that continue to drive this idea.

However, distinct from the romantic ideal of the long 19th century and the gentleman scholar/adventurers are the ideas of Marija Gimbutas. Archaeology in the '50s had moved (primarily through Gordon Childe's influence) towards a charting of population movements/migrations as the driving force of change, and Gimbutas took this idea to the extreme. She hypothesised that before the consistently patriarchic societies of the Metal Ages, there must have been a matriarchic ideal Neolithic society which she called 'Old Europe'. At the time, she did present a number of arguments that did drive scholarship for a while (though it was always a pretty shoddy piece of work, and I'm surprised it's not part of the /r/badhistory canon as much as the Von Danicken stuff is). Her work was quite fundamental to the modern feminine utopia-history of today.

Another, parallel route is Marxist history. Marx also assumed an utopian 'ur-condition' for mankind, which had to pass through the feudal and industrial states to the new communist utopia. Marx as a historian was incredibly influential for his materialist views, though this deterministic train of thought was more a product of his later, more radical phase and is not good history (though again, a product of its time).

Modern historians that think the prehistoric past was egalitarian are very likely to be influenced by either of these three movements, or a combination of them.

You mention "early writings". But in that case we are in the realm of history, not pre-history.

This is a question for /r/AskAnthropology. Most sources I've read make a sharp distinction between tribal hunter-gatherer societies and post-agricultural revolution societies.

It's difficult to imagine what archaeological evidence would support the idea of an egalitarian social structure, given that we're talking about pre-literate societies. All one can do is extrapolate from modern hunter-gatherer societies.

Here's what I've gathered from reading about modern hunter-gatherer tribes: They often have a relatively egalitarian social structure, which proceeds naturally from co-operation in the hunt. They think of themselves as members of a tribe, and their sense of individuality is not well-developed. The tribe is usually thought of as descended from an individual (real or mythical) or a totem animal. Labour is necessarily communal.

These social relations do not extend to relations with other tribes, which are often hostile.

This is in sharp contradistinction to the post-Agricultural Revolution societies, such as the ones in Mesopotamia and Egypt, which were able to support a priestly caste on the agricultural surplus, and typically had a pyramidal social structure. Only then do we see the rise of states and of organised warfare, because the agricultural surplus was able to support specialized occupations and division of labour.

You are right to be wary of projecting political biases onto the past. But you should also be careful that you do not do that yourself.

I honestly think your question holds a false assumption. Many historians are well-versed in anthropology and know to not confuse matrilineality with a matriarchy. The first one is not that uncommon throughout history, the latter one is mostly unheard of. Those few instances where woman were the head of a household, they were mostly replacing men and treated as men. Gender division based on biological appearance wasn't as clear cut as it is in contemporary times.

"It's especially galling because contemporary hunter-gatherers are hardly any of those things"

Au contraire! Which is why this fallacy comes up all the time. A lot of folks conflate contemporary hunter-gatherers and indigenous societies with "primitive man", and thus assume that because something is present in those cultures, therefore it can be generalized to prehistoric humans. However, just as there are some indigenous cultures that are matrilineal and some that are not, and some that are egalitarian and some that are not, and some that are pacifistic and some that are not, surely during prehistoric times the same would have been true.

A major reason for conflating egalitarian social structures with "prehistoric humans" is the huge amount of ethnographic research done with the !Kung and Khoisan peoples of the Kalahari desert starting in the 1960s. They are an example of an egalitarian hunter-gatherer society. However, their existence doesn't generalize to all hunter-gatherer cultures, let alone hunter-gatherer cultures of the past, much less prehistoric humans as a whole.

So far a lot of the responses here have come from anthropology but I think the main part explanation here may ultimately be located on another level - namely Rousseau's idea of the noble savage and more generally the convoluted temporality of modernity and modern thought which tends to situate itself on a caesura, a gap, between the ancien regime for instance and the neuzeit. This conception ultimately is religious - hence the desire to identify a kind of Eden operating "before history began" 10,000 years ago or in the jungle. If a "pure" human society could be found that did not suffer from our evils this would obviously make things easier since it would suggest these evils aren't inherent in the 'bad animal' of Man.