You can think of alma mater as a school seen as the mother who fed you and brought you up. You grew there, then you left, and the place stays behind, still counting as yours. That is why the word almost always belongs to someone: it is my, her, or his alma mater, never just a school on a map. Once you can see that mother standing there, the second use follows easily: she has a voice, and that voice is the song everyone stands up to sing.
From the word’s history
Latin alma mater means literally 'nourishing mother'. The phrase comes from the full name of the University of Bologna, the oldest university in Europe, which calls itself Alma Mater Studiorum, the nourishing mother of studies.
拉丁文 alma māter 字面就是「滋養人的母親」。這個說法來自歐洲最古老的波隆那大學：它的全名裡有 Alma Mater Studiorum，意思是「學問的滋養之母」。所以今天說 my alma mater，裡面還留著「養育我的地方」這層意思。
Wiktionary entry for alma mater, supplied in this batch's evidence packet (source_ref kaikki:3f6f69a190036ae4:1391468329).
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