I think it's easier to support this concern the older you get. Here's why: as you age, you begin to see documentaries on TV and YouTube that expose widespread government coverup and misinformation operations from the past, (and this is crucial) about episodes through which you lived. The obvious example for me is the nuclear industry. A concrete example: in the 1970s we were told that nuclear power plants were entirely safe because a) they have control rods to stop fission and b) they're safely contained. As an engineering student I would have happily told friends and family these things as received facts. In reality a) post-scram the reactor carries on dissipating megawatts so it will easily melt and b) all sorts of gas and liquid under pressure needs to be vented from the containment system and c) some of those gasses are explosive, so it isn't able to contain. Fukushima nicely illustrated these factors. Iterate this a few times and you end up with this uneasy feeling that nothing you're told with authority can be relied upon. Having gone through the experience of believing something then discovering it was a lie feels different than someone just telling you that governments and authority figures lie.

Not saying here that one should avoid the vaccine, just that experience shows that a healthy skepticism is warranted. Do your own research and draw your own conclusions.