Tobi was chosen.
There is a high possibility , that Tobi is the closest relative to Izuna and Uchiha Madara still living.
Tobi was saved by zetsu and improved by Hashiramas DNA.
Madara told Zetsu to keep an eye on the later descendants of Izuna.
Tobi sayed , that he gave Nagato the rinnegan , and the eyes belonged to him.
I think , that Tobi meant by that = that hes great grand father gave hes MS to Madara = and Madara gained EMS and Later Rinnegan thanks to it.
Tobi was closest relative to Izuna and thought of the eyes as his will of hes great grand father.
This information was kept secret by the village elders = Hiruzen and Even Minato was aware of this.
Danzo was aware of this aswell = and later on they cooperated on the Uchiha Massacre.
Zetsu told Tobi about the secret hidden past of the Uchiha and how the Uchiha clan betrayed Madara Uchiha.
Later on Tobi took the name of Madara Uchiha to aveng the shinobi world with hes name = in honour of Madara Uchiha and Izuna.
and so on.