This is simple. Giving is voluntary. Some people Went to such-and-such a school. They needn't give. Others are Members of the Alumni for such-and-such a school. They should give generously. It's entirely up to you to decide whether you simply paid for a certain education, or whether you entered into a life-long association with your school's institutions.
edit: I know it sounds snarky, but I mean it in a curious way, inspired by your 'life-long relationship' phrase. Is the school vetting you for life, or is it a one-shot irrevocable deal? Can a school revoke a degree for incompetence (...where it was obviously a mistake to award the degree in the first place)? What about discontinued financial support?
The tuition is purchased, the degree is earned, membership in a social group of Alumni requires participating in its support.
I see that I was remarkably unclear, even for me. What I mean is that if you go get your degree from Harvard, you are always entitled to it, without paying another cent. But if you are the type to fraternize with the administration, attend games and other events, and describe yourself as a "Harvard (Wo)Man" in the present tense, you probably ought to support it just as you would support any other type of club that has ongoing expenses.