The "correlation doesn't imply causation" argument doesn't really work here since there's a clear cause and effect link between the two variables in question.
I know that it all makes perfect sense in your head, but that does not reflect, or account for the pitfalls of how data is collected. For example, there is a possibility that people tend to get more ill in the winter in general, and it might have an impact on tests because they are not perfect. Also, even when there is a clear cause and effect link, you still have to know how strong it is to get meaningful information. Choose a number. The more you test, the more infected you get.
Apparently an overly aggressive response is a problem in particular with covid because it's in your lungs?
Imagine you have several different protection systems but most of them don't work well, then the one that does tries to compensate for them by working in an overdrive, causing an overreaction. In this case it can be fatal because it stops the flow of oxygen.