The immense pressure is the women's own doing. Women largely prefer to partner with men who make more money than them, so naturally if one partner becomes a stay at home parent it makes more sense economically for it to be the woman.

If women don't like the pressure to be a stay at home parent, then women can start marrying men who make less money than them (men don't as a group place little value on their partner making more than them) and instead face the pressure of providing for their family.