What is "the final problem"?

 (Sherlock meta by ivyblossom)

fencingwithherself:

Hello! As one of the few in my dash that actually liked TFP, and someone whose incredible analysis were my gateway to the fandom, i was wondering if you could please help me understand. With the episode as it has unfolded, what would you say "the final problem" was? Can it be like, verbalised in three or four sentences? Did it got resolved or even addressed? Because i' m lost at this point.

Ivy Blossom:

Oh, sure! The final problem can be summarized in a single word, in fact: the final problem is Sherlock.

The feat of deduction in The Final Problem is also the case at the heart of the entire show: why is Sherlock the way he is? Why does he want to be a sociopath? Why does being alone protect him? Why does he believe himself to be so unloveable, never anyone’s best friend? Why is he so obsessed with solving crimes? What made him what he is?

Sherlock himself is the final problem. And solving it helps him resolve his own internal contradictions and accept the parts of himself he has been rejecting most of his life. Solving the final problem makes Sherlock whole.