Three-eyed crow and the last Blackfyre pretender

[Lord Varys]

The raven may given us some hints that Jon Snow is actually Rhaegar's son, but I don't see why we should deduce from that action that he wants to put Jon on the Iron Throne. That no longer possible. Jon forfeit all his rights when he spoke the words. This cannot be undone.

My guess is that Jon's heritage comes into play in the fight against the Others. Which is why Bloodraven pulled the strings to make Jon Lord Commander. He may also feel connected to him if he truly is his great-great-great-great-grandnephew.

There is also still the chance that Bloodraven is mistaken about who is Azor Ahai. We don't yet know if Bloodraven did see the birth of Daenerys, and even if he did, could he see the birth of the dragons and what she has done since then? Bloodraven indicated that Bran would eventually be able to explore pretty much everything in the past, but does the weirwood network extend into the Dothraki Sea, Qarth, and Slaver's Bay? I'm not yet sure about that. Bran and Bloodraven will eventually find out about her, but do they already know? If not, they may actually assume Jon is Azor Ahai or at least the best candidate to become Azor Ahai.