Why would she get a ticket over his immediate family? 

It’s not always easy to decide who gets to attend your graduation. Many high school and college graduations limit the number of family members who can attend per graduate. If you only have a handful of people in your immediate family, you probably don’t have to pick and choose exactly who gets to attend the ceremony. If both of your parents have eight siblings and so do you, it’s going to be pretty harrowing deciding exactly which aunts, uncles, and siblings to exclude from the occasion. 

An uncle you see once a year might be relieved that there aren’t enough tickets for him to attend your college graduation, because he didn’t really want to attend anyway. A family member who thinks they should be invited, like your dad’s new girlfriend, might be less forgiving if they feel they are entitled to attend the graduation of a kid they aren’t even related to. The young graduate in this story is not about to put his dad’s girlfriend of less than a year over his mom, brother, and grandma, but his dad sure wants him to.