There's an article circulating on the net claiming that "before patriarchal times" Friday the 13th was a sacred day for women to honor the goddess and to celebrate their menstrual cycles. However, the time period generally considered "before patriarchy" was the stone age in Europe when goddess figurines like the Venus of Willendorf were made, that is, 7,000 BCE to 9,000 BCE, and / or pre-Minoan Crete, before approprixately 3,000 BCE, which was also the stone age. Friday the 13th didn't exist before the application of Germanic derived week names to a Roman-derived calendar system, which did not happen before approximately AD 200.
The "fri" in Friday is from the names of heathen goddesses Freya or Frigga, and the artwork illustrating your article is Freya. These are two of the major goddesses of heathenry, commonly called Norse mythology. The Old Norse calendar had every month starting on Sunday, and every month had 30 days (with some extra days added in the middle of summer) so days of the week didn't change number every month like our calendar does.
The names of days of the week in modern English come from the names of heathen and pagan gods. The calendar system we use in modern English speaking countries is the Gregorian calendar, which replaced the Julian calendar. The Julian calendar was named after Julius Caesar, and the Gregorian was a Christian calendar named after a Pope. The Christian calendar is based on a pagan Roman calendar, which was adopted by Germanic tribes having contact with the Roman Empire, and who applied their names of Germanic gods to a calendar system that already had the names of Roman gods applied to the days of the week. Before the adoption of the modern calendar system, in which the name of the goddess was adopted into a calendar system with rotating week and month start days, it was impossible for the name of Frigga to occur in the same calendar as a calendar in which the day of the week on which the 13th falls varies. Friday the 13th is a product of our modern calendar system.
Both Friday and 13 were considered inauspicious starting in medieval times. However, Friday the 13th was not considered especially unlucky until the 19th century.
The claim circulating on the net that the Patriarchy stole Friday the 13th from women is simply not true. There was no such thing as Friday the 13th before patriarchal times.
Image: Gregorian Calendar page via Wikimedia Commons