You go to church with a purpose: attending masses, praying..( you are ,say, a Catholic..).
You are not a Catholic(supposed)(or even you are one, it does not matter), you go to THE church to meet someone there.(you have no intention to hear masses(there and on that day).
So, it will be the same way to use THE with Hospital, school..!( You are at school because you are a student_ You are at THE school to wait for someone, to meet someone or to pick someone up...You do not study there at that time..).
THE University of San Diego tells us what university, which has been defined by "of+noun", therefore it needs THE for clarity.
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