The problem with talking about vaccines these days is that it became a very polarizing emotional discussion, when it should be a nuanced rational one. This subject has been co-opted by politics, and misinformation is abound. People who have never read a scientific paper in their lives talk with full arrogant confidence about what is and what isn't.
Vaccines are legitimate and have saved countless of lives since their invention. Nevertheless, vaccines are distributed by pharmaceutical companies which have been involved in
a lot of shennanigans, leading some people to be wary. Also very troublesome events such as when the
CIA faked vaccination to try and find Bin Laden have also certainly not helped making people trust vaccination campaigns.
That being said, most of the fears people have of vaccine are exaggerated, based on misunderstandings or completely unfounded and based on fake news.
This great wiki entry goes over some of the fears and counter-arguments.
Now specifically about COVID-19 vaccines. Generally, the process of developing vaccines takes many years, decades even, due to regulatory issues but also due to the necessity of extensive testing of tens or hundreds of thousands of people over years to get a full picture of the possible side effects. With COVID-19, due to the emergency situation, this process had to be significantly sped, which on one hand meant an unprecedented level of medical research and development, but also, meant the difficulty or impossibility of seeing all the potential side-effects in the first moment. We are still learning things about this disease and vaccine.
From a public health policy stand point, it seems the right decision was indeed to facilitate and speed up vaccine research and production, and do mass vaccination of the general population with whatever vaccine passed the 4 stages of research with good results.
From an individual stand point, though, not all vaccines are necessarily equally desirable for all people. As an example, the AstraZeneca vaccine was linked to a certain number of deaths due to blood cloth, specially in young women. This information was not clear from the initial research with tens of thousands of people, but became apparent during actual application in millions of people. On men, and specially older people, that risk is practically non-existent. Some countries have changed their policy regarding this vaccine to adjust the application to the less risky population, which IMO is a correct decision. I don't think the policy-makers are to blame for having earlier accepted vaccination to all people including younger women, since this information was not available at first, but what about if someone in your family, your sister for example, was the one that died after taking the vaccine? No amount of statistical justification will bring her back and make you feel at ease. At the same time, how many people's lives were saved that could have died otherwise, but since this is just a statistical information, it doesn't register in our brains as easily. If you could know that a loved one has only been saved due to the vaccine and otherwise he/she would have died, you'd be way more pro-vaccine, but this information is hidden by its very nature.. That's something the people against vaccines don't see.
Another issue that makes this subject more complex, is that the vaccine discussion is mixed with the discussion of public policies: mask mandates, lockdowns, travel restrictions, etc. Generally people fall into two camps, pro vaccine and everything else, or anti-vaccine and everything else. But this can also be nuanced. Someone can be pro-vaccines, but think generalized lockdowns lasting for years do more harm than good, and that masks are good practice and should be done when there are many people but that masks being obligatory wearing outside is senseless, etc etc.
Me personally, I have taken my two shots of Pfizer vaccine. I have measured pros and cons, and think it is very very clear that there are way more pros than cons. That being said I don't think people should be forced to take, but rather people should be properly educated so they can take their own informed decision. For those interested, reddit.com/r/covid19 is a strictly scientific subreddit where peer reviewed papers about vaccines or anything related to the disease are posted and commented on, it's a great resource to learn.
Lastly, as for dithyramb's comment on natural medicine vs covid... The problem here is that you cannot know from subjective judgement whether it worked or not. It is silly to be sure something cured you because you "felt good afterwards", if this was not a part of an actual research with proper statistical analysis. Which doesn't mean it necessarily doesn't work, but it is merely a hypothesis at most, a dangerous fantasy and misinformation at worst. While one may decide to do it oneself since we are all sovereign individuals, I certainly wouldn't talk about it with certainty or "spread the word" to others, at least not with due disclaimers/caveat.