The Patriarchy is, for the feminist, an external locus of control, that is, the thing to be blamed for all the world's problems, and often their personal problems as well.
The Patriarchy is concerned with the fact that feminism is at war with the housewife and by extension, with the institution of the family.
The Patriarchy is not a system that values men over women, as evidenced by the fact that men die in wars, die in 92% of workplace deaths, do dirty jobs, are at a disadvantage in custody cases, and are expected to support their families at all costs to themselves.
The Patriarchy is loosely defined as everything that is not feminist dogma. It is a conspiracy at all levels of western civilization designed at every turn to control women's lives and hold them down as second class citizens.
The Patriarchy is indifferent to identity politics. It cares little if one is a man or a woman, it cares only about getting the job done.
The Patriarchy is a system that recognizes that anyone of either sex will be miserable if forced into a particular role they are not suited for... it just so happens that because feminism vilifies women for staying home, or pressures them to study a particular major just to make the sisterhood proud, women have become intensely unhappy over the last 35 years.