Something that helped me is this thinking.

You cannot guarantee that the violinists have are not good at playing.

There is still a chance that all violinists at NYC are not in that group of not good at playing.

Even if this chance is really small, there is still a chance that 0 NYC violists are not good.

From my understanding

Swimmers -> Jacksons means that for you *to be a swimmer, you must be a Jackson

*Yet, you can be a swimmer and not a Jackson, so that conditional logic does not work.

Instead

Jackson -> swimmers, with the contrapositive being /Swimmer -> /Jackson

The reason is, if you are not a swimmer, you are not a Jackson, which is what the original sentence was.