Because vaccines were typically developed slowly and carefully.. but with Covid, due to urgency, several aspects of testing were run in parallel, to reduce timescales. I don't claim to understand the rest, but these newer types of vaccines are simply quicker to create, modify and test.
Also, you are confusing the time it takes to assemble volunteers, test the vaccine on them and produce results, with the timescale of any side effects. As I understand it, there is no correlation, and any side effects tend to be pretty quick to appear. In my case, I felt a bit shit after the first AV dose. Chills, poor sleep, headaches, for a few days. But compared to what a few acquaintances have experienced with Covid... it's nothing.
My youngest daughter's partner has so far refused the jab. I'm not happy, but I can't force him. They have a 3-4 month old baby. Daughter refused the jab while pregnant..I can understand that, because the urge to protect the baby is all consuming, but it was reorted early on that the jab did not harm pregnant women, and could even protect the unborn baby. She's now had the jab.. twice. AFAIK, partner hasn't had it yet. His seems to be a mix of a general Carribean reluctance, his reliance on The Lord.etc.. The weakness in his argument is that he intends to get the jab 'When he is ready'..but 'He is not ready yet.'. So... what will make him ready?
Also sadly.. reports indicate that pregnant women are presently one of the major groups of unvaccinated people dying from Covid.