Why do we use "catch" for describing a contracted illness

Not a native English speaker but my native language also uses this phrase. I would say it does originate from the old belief that diseases, in general, are contagious, i.e. when a person got sick, they were "throwing" the disease (no matter how people pictured that centuries ago) around themselves, and others could "catch" it.

Its senses in early Middle English also included "chase, hunt," which later went with chase (v.). Of sleep, etc., from early 14c.; of infections from 1540s - https://www.etymonline.com/search?q=catch

Given that this usage goes back to the 1540s, I think it could make an interesting research question for someone with knowledge of English in that era. I don't believe a short, Google-searched answer will resolve it.

There doesn't appear to be much happening in the way of disease in England at the time. This was not long after Henry VIII executed Anne Boleyn and just before Copernicus set forth his theory that the earth revolves around the sun.

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I'll just note that these days we often talk about "getting a cold/flu" etc. That also seems to build on the idea that we somehow actively obtain an illness. Why? I don't know.