The Nerva-Antonine dynasty was arguably the most stable period in Roman history, largely in part to the stability that the adoptive emperor tradition brought with it. So why is that Marcus Aurelius allowed Commodus to ascend? Being the philospher king of Rome one would think he would have prevented Commodus; a military and poltical outsider, from ascending.
Was it because he was the only of Five good Emperors that had a living son to take over after his death?
Did his stoic philosophy make him believe that Commodus would rise to the occasion? "Nothing happens to anybody which he is not fitted by nature to bear." Meditations V.18
I've read meditations but he doesn't seem to give much insight into his philosophy on family or succession. I haven't read Cassius Dio, is there more insight in that text?
This is kind of a boring answer, but Marcus Aurelius was the first to produce a male heir. Although succession-by-adoption has a long history of being considered the "best" form of monarchy in the classical world, there isn't really any firm reason to believe it wasn't just accident.
So this answer might be sort of underwhelming but from what I've read and understand Marcus Aurelius allowed Commodus to succeed because (drum roll, anticipation, build up)... he loved his son. Often time we get caught up in the image we have of figures in antiquity and their greatness and all that and forget that they were men. Yes, the preceding emperors adopted their successors and chose formidable heirs but Marcus Aurelius apparently had faith and his son which allowed him to see past Commodus' flaws.