Not exactly, you don't deserve to get dick days for your child being sick if you have no child.
Also you deserve additional leneancy when your child is sick. Cannot plan for that. They just do that and need more supervision than your sick partner.
Most things that reduce non parent's ability to work can happen to parents equally.
Vacation does in fact suck though. A lack of child shouldn't make it harder for you to take a vacation. But your employer also must enable parents to take time off when their kids need supervision, so that sounds like a staffing issue.