Donating to your Alma Matter signals that (1) you succeeded and (2) that your Alma Matter helped you succeed. Given enough donations, this boosts your own prestige.

Or, reverse this: if I go to a school and that school suddenly starts to suck, then I will be tainted with the school sucking.

Either way, it's a problem of credentialism.

My college did a lot of good for me, and the staff I interacted with seemed to be working below-market because they believed in what they were doing. It's a non-profit institution so I expect they would spend donations on something that they thought (rightly or wrongly) furthered education rather than just giving them to someone. And what I paid at the time was subsidised by previous donors and the government, at a time when I couldn't've afforded to pay much more; now that I've done well in life, in a way that seems at least partly off the back of that education, it seems fair to contribute something back.

I donate to my university, I do it to fund scholarships and programs that I benefited from when attending. I don't donate to the 'general fund'. Although the bulk of my donations to my alma mater go to cancer treatment center at the university medical center which relies on fundraising for research and other programs which I believe will benefit all. I would never donate to revamp a student union as I believe that should be paid for by the University.

Money is fungible. Every dollar donated to the medical center is a dollar freed up from the general fund (until the medical center is totally funded with earmarked donations, of course).