Board Thread:Naruto Discussions/@comment-29393962-20161111215453/@comment-734582-20170119180135

Elveonora wrote: Why Kurama though I guess that since Kurama is the biggest portion of the Juubi, he's sort of representative of the Jinchuriki side of Hagoromo (since Hagoromo was Juubi Jinchuriki for a very, very long time). So Ashura = body, Indra = mind, Kurama = spirit (ie, a trinity) and so reinforced Hagoromo's chakra enough to summon him.

Naruto and Sasuke both met the conditions: Notably, Sasuke was in contact with Kurama not long before (ie Majestic Attire) and got Hashi cells (though personally i think they're zetsu cells, explaining the absence of Wood Release. Same goes for Naruto's prosthetic).

Naruto obviously met two of the three conditions in life. He could've gotten Indra chakra from Sasuke (IE Majestic Attire) or Madara/Obito. Black Zetsu noted that the Transmigrants were usually not so cooperative, so it's likely that Sasuke's Majestic Attire allowed both to meet the conditions. Considering they were both busy fighting though, it's probable that they weren't aware of the connection until they were near death. Alternatively, it was Naruto becoming pseudo-juubi jinchuriki and Sasuke getting Hashirama cells that strengthened this connection to the point Hagoromo could communicate.

As to the Rabbit similarities, i think it's simpy a side-effect of Ashura. When Kaguya went out of control, Kurama's face looked somewhat rabbit-like. I guess that the Rabbit is the Otsutsuki clan animal (also since it has connections to the Moon) and since Ashura is an Otsutsuki, Kurama's avatar morphed.