Is the world progressing and moving towards having a Global Matriarchal Society to replace today's ....?

No. Basically what is going on is that the social order is being disrupted in as many ways as possible (the family unit is being disrupted, children are being corrupted, our food and water is being poisoned) not as an end goal, but as a means to an end, the end being a global communist society - neither matriarchal nor patriarchal, but one where there are workers (men and women alike) and then the elites who control everything. What you see now is just a stepping stone towards that.