They say x, ask for where they heard about x. They say from y news organization, ask the source for y. If they say z, if z is actually an actual document or otherwise, ask them where in z does y claim x is true.
If z is just another news organization, keep going until they provide (or don't provide) an actual document. If they can't procure an actual document, send it yourself. If z is just another video cIip, ask them for the whole video. Provide them the entire video if they can't.
Do not try to antagonize. Just simply ask the questions as if you were trying to understand their point of view, to learn something we might not have heard.
You have to use the same 'logic' they are using. Ply them with bullshit anecdotal stories. The fellow posting pictures over his son's casket after the pfizer shot. The athletes falling over. The kid who isn't worried about covid, but wears a mask because he feels ugly.
But honestly, you can't win. My inlaws watch government sponsored news for an hour every night. How can I, the 'child' of the relationship, convince anyone in a way that tried and tested propaganda won't erase in a few hours?