Parents are a voter group.
Parents are citizens who have children. The safety and welfare of their children is a parent's primary concern, so the group advocate for laws and subsidies which help look after the well-being of kids.
Parents can't be retired.
A lot of the policies parents want benefit the poor and the youth and are supported by socialists, though are seen as wastes of money by capitalists. Parents are sensitive to issues of morality and safety though; they often seek to restrict social freedoms to protect their children, upsetting liberals and often aligning them with religious and conservative elements of society.
Parents don't have their own pressure group.