Why did families change from extended to nuclear and patriarchal to egalitarian?

The industrial revolution. No longer did families rely on numbers to generate acceptable living conditions: under agrarian societies the more kids you had, the more workers you had to help you make profit. With the 'rise of the machines' one person and a machine (say cotton jenny) could do more work than 5 people alone could. This did cause raw manpower to become less valuable, but there were always new opportunities (repair the machine, sell the machine, make the machine etc.) The actual value of a child as a worker went down. So the next thing that happened was education: no longer were you absolutely stuck on the farm, you could take your education and go somewhere else.

In a nuclear family an extended amount of time and energy is expended on a smaller number of children.

As to patriarchal, there was no longer a need for a single point of responsibility, others in the nuclear family had much more of a stake in the governing of the family.