It's kind of nuts how integral Onyxia is to Anduin, even when she was a villain that's been dead for damn near twenty years now in real life, and it's even kind of nuts how this is all just... never addressed how much she deeply affected him.
His mother is dead because of her. He will never know her, losing that crucial relationship from Onyxia's petty scheming. His father, in response to this tragic death, had pulled away in his grief and depression, and when he finally started coming out of it—coming out of it because of his love for Anduin—after nearly a decade of having an absent father, he's taken, stolen en route to Theramore, no ransom demands made, nothing. After just getting his father back, he's gone again, Anduin unaware that it was Onyxia's plotting.
He comes back, and he comes back different, not fully there. Anduin suspects him an imposter as he continually presses his father for information about his kidnapping, which he cannot give good answers to, but Onyxia missteps, tries to kill Anduin, and his father, full of the love for his son even in his somewhat absent state, full on throws himself off a cliff to rescue his son. That's his father.
It comes crumbling down for Onyxia after that, as the other half of Anduin's father comes stomping through, all of that missing spirit and rage, focused solely on saving his son. Both sides come together when Onyxia lashes out and takes Anduin, intent on either using his bloodline for her plans or feeding him to her children, and rescue him, those two sides being joined together again in the process.
But it's not all well and good afterwards. Anduin's father is still different—volatile as he struggles to still be joined internally, and Anduin's hitting his rebellious teenage phase, leading to constant problems in their relationship. Even in death, Onyxia was still pulling them apart, and it takes his father nearly dying for them to reconcile, something that apparently is a constant struggle from them afterwards, considering Anduin later has to reassure to himself that they did reconcile.
And when Anduin's forced to lose control of himself, forced to act in accordance with another's will, so wholly and utterly that he doesn't even know if his emotions were his own or not, what is the vessel of his domination? What is that which binds him so?
It's his father's sword, a sword that would not exist if not for everything that Onyxia had done.
And once he's free, he still carries it with him.