you are correct, you are not proving anything
to wit, you have not proven there is a good reason to worry about widespread significant long-term side effects of the COVID vaccines -- specifically, DDT is not a past example of a vaccine resembling any of the COVID vaccines
the lack of evidence pointing to widespread, significant, long-term side-effects so far, however, is evidence enough for us to lean in that direction
I do, however, support your right to avoid the vaccine, as well as your right to avoid any place or activity that requires those present to have it, so at least there's that