Probably the biggest one is that I do not believe that punishment is an effective deterrent most of the time. People will keep committing crimes even if the punishment is harsh.
Another is that our prisons need to be less about punishment and more about rehabilitation. A punishment-heavy criminal justice system creates more recidivism, people leave prison worse off than when they started, they might enter as petty offenders and leave as "jaded, hardened criminals".
Another is that many crimes are driven by the perpetrator having issues with poverty, drugs, etc., which should be addressed differently.
Another is that prisons are already overcrowded, underfunded, courts are not efficient, etc., so adding more felony convictions makes those problems worse and is expensive.
Another is that reformed felons have trouble finding employment when they get out. In some states they lose their right to vote.
Another is that some people are falsely accused and falsely convicted, or, I've heard this is most common, charged in excess of their actual involvement in the crime.
Another is that sometimes accused criminals have families. When you traumatize the offender's kids, you may create more criminality in the kids.
These are a few, expressed briefly and quickly. Others can probably explain it better, or with more time put into reserach.