Disclaimer: I’m an introvert, so that should explain why I don’t get something like this.
Whether it’s posting your acceptance letter on Instagram or screaming your lungs out in a full body suit with your school’s colors at the NCAA Final Four, I just don’t get what’s so appealing about the whole thing.
Many people enjoy feeling part of something. The connection with each other as well as pride in an institution means that for a lot of people. For many schools it extends beyond the school and includes state pride, national pride, and international pride. Feeling connected is a human need for many.
Well, my user name is related to my university’s mascot, so I guess I’m guilty of college pride! I really enjoyed my years at UT-Austin and think I got a top-rate education. I like bragging on the school. And I do feel a connection to other people who attended the school. When I (very rarely) see a car with Texas license plates here in Maine, I pull in front of it so they can see the Longhorn emblem on the back of my car. 
Humans are tribal beings.
“The evolutionary Rubicon that our species crossed hundreds of thousands of years ago that led to the moral hive mind was a result of “shared intentionality,” which is “the ability to share mental representations of tasks that two or more of [our ancestors] were pursuing together. For example, while foraging, one person pulls down a branch while the other plucks the fruit, and they both share the meal.” Chimps tend not to display this behavior, Haidt says, but “when early humans began to share intentions, their ability to hunt, gather, raise children, and raid their neighbors increased exponentially. Everyone on the team now had a mental representation of the task, knew that his or her partners shared the same representation, knew when a partner had acted in a way that impeded success or that hogged the spoils, and reacted negatively to such violations.””
https://www.scientificamerican.com/article/evolution-explains-why-politics-tribal/
So another form of tribalism is the tribe of our college. College sports is a stylized way for our “tribe” to fight against their “tribe”. Posting your acceptance letter is letting everyone know what tribe you are joining (and everyone is asking so this is just a way to tell everyone at once).
OP: I understand your position. But many others feel a need to belong to a group. College pride, belonging to a group, blindly believing in a cause is mentally healthy for most people.
You can have school pride that doesn’t extend to face painting. My UMiami friends Facebook comment the games and talk trash with our friends who attended other Florida schools. It is fun and we also have “Florida Rules”, where we will support another Florida school against out of state competitors.
School pride makes you buy school gear baby clothes to brainwash the next generation. My children had it all - bibs, tiny socks, onesies, cheerleader outfit, etc. People decorate their home offices and game rooms in school colors. I’ve got the license plate holders. (Family loves to feed the obsession with UM related gifts.)
I think it’s nice to be proud of your school and its’ accomplishments in both sports and academics. I’m sure not everyone feels that way but I don’t see anything wrong with those that do.
Then you’re just a poser. 
It’s about having fun and enjoying life. If you have ever been part of a tournament run in basketball, national championship race in football, etc. its nuts. Sure beats studying.
“posting your acceptance letter on Instagram” is much different than screaming idiotically.
Posting an acceptance letter is a reflection on the fact you have worked hard and you’re going to be able to move forward with the next step of life, college. It has nothing to do with being extroverted or introverted.
As for school sports spirit, I’m one of those people who could really care less. It does not benefit me whatsoever if Drexel beats Villanova in basketball. I don’t go to any of the games, because I’d rather be at the gym, be playing video games, or drinking in peace at home.
Sharing an enthusiasm for something with other people is really fun, forms bonds, and confirms our choices. School pride is an easy one - hey, we all go here, so we have something in common! It’s OK to be a super-dorky fan about something in your life. Maybe your school doesn’t turn your crank this way but a TV show/genre/video game/hobby/sport/ does.