Please don’t post vaccine skepticism for the sake of vaccine skepticism. If you have some sources from medical professionals with legitimate concerns that’s fine, but this is a dangerous oversimplification for something that’s life saving.
I would separate two kinds of vaccine skepticism. One is the anti-vaxxor mentality of rejecting the premise of vaccination.
The other being that this new vaccine is developed so quickly that there hasn't been time to check for long term effects (in the order of years). Most existing vaccines took years to develop, and this allowed time for testing of long term effects.
I understand this second type of concern - the authorities need to put in some assurance about it, and re-ignite trust from those who are now very skeptical of the gov't and institutions. This skepticism can escape to other aspects of society - like trust in the election results, and other gov't institutions' neutrality and public good status. It is a crack in the system, which if not fixed quickly, could lead to the dam of democracy collapsing.
While we're asking questions, also ask yourself if the vaccine came in a pill form, would you be more likely to take it? If so, you might just have a intrinsic aversion to getting stabbed by a stranger, which is totally understandable but perhaps conquerable.