There are rational reasons to be hesitant even if on the whole, they don't fully add up (individual situations notwithstanding).
But the hesitancy I've witnessed is not based on a kind of logic or reasoning, rather just an 'instinct'.
If all you read is weird FB posts, tabloids then the sum totality of the 'decision' will just be 'no'.
Fox News I think illustrates how this can happen. Fox hasn't taken a Covid or vaccine denying position. In fact, you could probably find that officially they have been 'on the side of the vaccine'. But since so much of the coverage is questioning, cynical, downplaying and contrarian - and - they have not actually been overtly supporting the vaccine programs ... it's easy for people to be 'net vaccine hesitant' if that's their information source.
So while at the very same time that a news organization can be '100% technically correct' on everything, the channel might become noisy and the net result is lack of clarity.
My father doesn't have an argument about 'it was made too fast', it's more like 'Oh, there's that goddam Fauci again, telling us what to do!'. He personally dislikes Dr. Fauci, at least in part because of the media he's consuming.
He believes that coronavirus is real, and oddly, has even been in the hospital for some minor things where there were insane protocols he was more than fine with following (i.e. masks everywhere, everyone taking it seriously) - but at the same time, when the subject comes up he says 'Oh it's a bunch of bull**t' , kind of in a huff. Also - he lives in rural area that has mostly not been affected.
Public Communications is not about making just rational arguments - it's about information clarity, emotions, credibility, how much fog and misinformation is thrown about, all of the specious and frankly totally false bits of Social Media etc..
CNN went to somewhere in the Midwest and interviewed a bunch of people in a small town and they largely reacted the same way:
"We just do thing differently here"
"It's not a big deal for us"
"We just don't need it"
While the 'it was made very rapidly' logic (and other reasonable arguments) are sometimes made ... that's really not it.
That's why in a crisis, information discipline is so important.
I firmly believe that if Republican apparatus and media were very committed to vaccination especially with public messaging, then about 25% more Americans would be vaccinated.
Imagine if the President of the USA was using his Twitter to try to get people vaccinated. Imagine if he held 'vax rallies' where free tickets went to anyone vaxxed. Imagine if he asked Country Music stars to support the effort. Instead of 'technically supporting vaccination while publicly being cynical about it'. That's what it boils down to.