Unfortunately i believe that there is no satisfying answer on why this specific character must be dragonborn. In Morrowind for example you are informed that you character was born in a specific day under a specific star so you are sent in morrowind as a false nerevarine only to be revealed that you are the true nerevar. In Oblivion the emperor recognized you from his dreams so instantly he trusts you to deliver the amulet to Martin and in that way you play the crucial role in defeating Mehrunes dagon although the true hero is, in my opinion, Martin.

In Skyrim you are arrested at the border and by pure chance you survive decapitation. Not only that but for no apparent reason they trust you to go to bleaks fall barrow where it is revealed you are a dragonborn. What exactly is dragonborn and how your character became dragonborn is something that is not explained by the game

By birth. You were born with the soul if a dragon. A child of Akatosh, the Dragon of Time.

"Each event is precedented by prophecy. But without the Hero, there is no Event." -- Zurin Arctus, the Underking