For example, most academics who use quantitative studies to investigate the effect of jail sentences find that jail time increases recidivism rates. In other words, putting someone in jail makes them likely to commit more total crimes over the rest of their life as compared to simply being released immediately. This is one decent paper on this topic that isn't behind a paywall; Professor Ian Shapiro at Yale University can refer you to more recent, more damning papers. If you believe this evidence, it follows that pushing long jail sentences to cause specific deterrence is flat-out irrational, and should be discontinued.

It only follows if you focus on deterring convicted criminals from recidivism. How about deterring people from becoming criminals to start with?

Are you saying that "pushing long jail sentences to cause specific deterrence" should be discontinued (which makes sense, if the specific deterrence is deterring recidivism), or that "pushing long jail sentences" should be discontinued? (which doesn't follow - you have only provided evidence that long sentences don't fulfill the goal of deterring recidivism, not that it doesn't fulfill any other goal)