Not that guy, but I'll give you one viewpoint.
>To me, these vaccines have been as rigorously tested as they could be
Not for me. The fact is, the vaccines have been pushed through faster than any vaccine before. Anything foreign entering the body should be tested and based on solid evidence. Doesn't matter if it's an artificial heart, stent, prosthetic, or a biological agent like a vaccine. If decades of medical research shows determining a vaccine's safety takes years because of ethical protocols, then it takes years. The present vaccination campaigns are performing more comprehensive stage 3 trials on the general population because the risks are deemed acceptable. As other people have said in this thread, a person under the age of 18 is 50% more likely to die of SARS-CoV-2 vaccine complications than from SARS-CoV-2. The risk isn't worth it at this time.
Additionally, the technologies being used for the vaccines is still deemed experimental, specifically the mRNA ones. No mRNA vaccines have been deployed before, but now it's being deployed on the general population without public knowledge of any potential risks of this unproven technology ("unproven" meaning lacking a prior real-world deployment effort; a rocket engine is only proven when it flies, not in simulation). One risk with the mRNA vaccines is that they need to be kept extremely cold to preserve the mRNA sequences [1]. If the dose warms, good mRNA sequences break down into junk mRNA, which for all intents and purposes are random nucleotide chains. That ties into an above point: no rational person wants random mRNA pieces put into their body. Again, while all risk is relative, for my age group, the risk is not enough.
If you're well-versed in the science, I recommend reading this complaint [2] filed with the EU regarding Pfizer trial safety.
[1] https://www.reuters.com/article/uk-fact-check-mrna-vaccine-s...
[2] https://2020news.de/wp-content/uploads/2020/12/Wodarg_Yeadon...