So there are many reasons to think otherwise, but the simplest one is - Every single medication and vaccine that we've ever made has known side-effects. Not all side-effects are known right off the bat, and many take years to detect.
I work in vaccines, but I can't think of a vaccine that was completely recalled due to long-term safety issues of the top of my head. Most recalls happen because one lot or the other had some production issues. Certainly, vaccines are extremely safe by the time they get approved - because the approval process is careful, methodical and takes years.
However, in this case, if a COVID vaccine is approved by the end of this year or in the near-term, we won't have any long-term data, and so I do worry about those aspects, about the compounds used in the final formulation as well as the untested nature of RNA/DNA based vaccines.
A few places to do research for those interested:
https://vaers.hhs.gov/data/datasets.html?
https://www.fda.gov/vaccines-blood-biologics/safety-availabi...