The German word überzeugen – literally over-witness; more than enough witnesses – means to persuade or convince with plausible arguments, evidence, proof that something is true, right, correct.
überzeugen for Germans means to use rational arguments only, to appeal to reason, without attempting establish a personal (subjective, emotional) relationship with the target audience.
The German word überreden – literally over-talk; more than enough talk – means to coax, plead, cajole, browbeat, armtwist the other person to do something they originally did not wish to.
überreden for Germans means to use subjective-emotional argumentation, to appeal to the emotions, to the non-rational. Germans reject überreden. Germans expect überzeugen.