'The Neolithic' is kind of a broad period; we could be talking about anything between the rise of agriculture in the Near East around 8000 BC to the start of the Nordic Bronze Age in Scandinavia around 1600 BC. Because this is such a broad and diverse period, it makes just as much sense to look at contemporary or near-contemporary societies with similar lifestyles, as it does to take out one prehistoric society and project their data unto the rest of the Neolithic. In some societies, women and men would have been equal in terms of labour divisions when it comes to the daily practice of animal herding and agricultural practices. Significant perceived status differences might be unrecorded by archaeology, such as those represented in their ritual life. There is currently still some debate on whether Linear Ceramic Peoples practiced exogamy, looking for brides outside of the own community, but this does not directly tell you much about status.

Earlier proposed models like the stuff of Gimbutas, presenting Neolithic Europe as some egalitarian feminin eutopia, is completely unsupported by the archaeological record. Neolithic people had their fair share of violence in society, to which all society, women, children and men, could be subjected. We do not know, however, whether the perpetrators of this violence were strictly men or a 'warrior aristocracy' as in some later societies. Yet this still does not tell you whether status was derived from acts or warriorhood, from which women can be assumed to be excluded, or not.

That train of thought is from a very famous book by a German materialist, which tried to trace the appearance of the family and of the state by looking at his contemporary hunter tribes. It's very difficult to summarize. Bare essentials:

Amongst the Iroquois there are no fathers because fathers cannot be tranced. It's only the women who are able to create a family. And it's in their power to disinherit or to cast away their kids. They own their men. If they are out they'll be alone. Man cannot bequest or inherit anything. They spent most of their time hunting or doing any other stuff to keep their (foster)mothers glad.

This is called matriarchy - the rule of mothers.

But that's the Iroquois.

Amongst the all the transmitted scriptures - Bible, Vendidad, Manusmriti, Aristotle, Quran... it is always the woman who is regarded as property, as a slave, not the man.

And they all have suddenly all a concept of fatherhood.

Why does always happen at this point when people learn to grow crops?

... are you listening?