see, in that example, you made up a rule that anything you want will cause Z, but there's no actual scientific basis for the rule
you have to actually prove Y will do Z, you can't just claim something else did Z, therefore anything can do Z
Again, you lack a basic understanding of the scientific method.
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