There are many reasons to oppose vaccine mandates, especially for this particular vaccine.
Since it is clear that the vaccine doesn't prevent the vaccinated from spreading the virus the societal benefits are minimal at best. Therefore there is no reason to mandate it "for the greater good". In any event if something is mandated the question must be answered as to who is liable for unexpected and potentially catastrophic side effects - it simply isn't acceptable to say that people have to have jab and if it ruins their life then, gee, that's just too bad.
In the normal process of making a medical decision we can find information about the risks and benefits of a procedure so we can make an informed judgment. With this vaccine, that doesn't appear to actually be a vaccine by any traditional definition of the word, all we've got is endless political blathering about how important it is that we all take it with precious little information about possible side effects. We're already talking about three shots, four shots - where does it stop? And as Lammchen said above, it's particularly ironic when senior Democrats were very vocal about refusing to take a vaccine developed under Trump's watch, only to now turn around and demand that people must face ever-more societal exclusion for not taking the exact same jab.
At present what we have is a situation in which most of us face an incredibly small risk of serious harm from the virus, the jab that doesn't protect us from the virus comes with what appears to be a somewhat smaller risk of long-term harm from side-effects but it's hard to find accurate information, and the jab that doesn't protect us from the virus doesn't protect those around us from the virus either.
My personal risk assessment is very simple. Early numbers indicated a 0.02% chance of death if I caught the virus. I did catch it and survived it, so I figure natural immunity will reduce 0.02% to something smaller, but it's hard to say how much smaller. The best figures I've found indicate something like a 0.001% chance of severe side effects from the jab. The benefit to those around me from taking the jab is virtually nothing. Therefore there's little reason for me to take it. The sense that anything negative about the jab is endlessly covered up doesn't inspire confidence.