1. To befuddle, to confuse, to rattle, to mix up, to discombobulate: The problem is that if anyone tries to use logical explanations for some political positions, it just addles the listeners and makes their understanding more confusing than comprehensible.

While Rodger was walking along the dark street late at night, his brain was addled by fear of what might happen to him.

2. To rot, to decay, to putrefy: The eggs were addling because they were not refrigerated and were on the shelf too long.
3. Etymology: from a Middle English word from the Old English adela, meaning "liquid filth". It’s related to the German adel, meaning "urine, mire" or "puddle".