I don't think it's an issue of seeing illness as a personal failing - that's just dismissive and an unhelpful characterization.
People I know that choose to not get vaccinated yet are largely resistant to the 'do it for others' push because we've been told that the vaccine is so effective that the 'others' should be safe anyway, unless they've chosen not to get the vaccine too. That leaves these people with a risk assessment based solely on their own health, age, etc.
The "for the good of society" messaging has been very unstable, even moreso than normal for public health messaging. It's been a mix of: the elderly will take the vaccines because they're at high risk and then life can go back to normal. Then it became all adults need to take it to build herd immunity (the concept that in 2020 was supposedly some sort of a-scientific conspiracy theory), then it became life won't go back to normal even with high vaccination rates, then passes were introduced that have an exception for testing i.e. they look like an attempt to stop spread of the virus, but then it became clear that vaccines don't stop the spread yet the passes remained the same or even had the testing exemption removed. Then it became something about hospital capacity but they started firing healthcare workers en-masse, then it became all teenagers need to take it to stop schools closing and/or to protect their mental health (UK justification), but schools closing is itself a government/union policy, now Pfizer is trialling vaccines for babies. So who knows what the justification for that will be. But, we can be sure they'll find one.
It's been less than a year and that's not even all the changes in vaccination messaging, just the ones related to why everyone has to take it even if they don't personally want to. I'm honestly not sure I even got them all. That's been combined with very strong messaging that anyone who doubts the perfect omniscient competence of the public health establishment are crazy loons who need to be purged from society, with some of the nastiest and most aggressive tactics deployed by western governments against their own peoples for a long time.
Really don't see a way to recover trust in vaccination after the rollercoaster messaging over this year. There's no consistency anywhere which strongly implies the collectivist goal is chosen, then scientific-sounding justifications are invented to justify it. By next week this comment will be out of date and more stuff will need to be added to the list.
People I know that choose to not get vaccinated yet are largely resistant to the 'do it for others' push because we've been told that the vaccine is so effective that the 'others' should be safe anyway, unless they've chosen not to get the vaccine too. That leaves these people with a risk assessment based solely on their own health, age, etc.