US to require COVID Testing for International Flyers

I have wondered about testing in any form for any purpose for about the same reason.

Realize that I read the Los Angeles Times daily, but don't have a television so don't watch the news.

If I were to have a test today that came out negative and made me "safe" to board an airplane or whatever, what would keep me from being exposed to Covid on my way out of the testing site and be contagious in a few days???

I must be missing something here.