we see the juubi has rienngan (spelling) plus some kinda sharingan (a bunch of tomo's) so this is my theory
what if when the sage fought the juubi he didn't have the rienngan and by sealing it in himself he got it but it wasn't the same as the juubi's
and his son (who's descendant's were uchiha) got the sharringan part of the juubi
(if u ask why didn't the sage get the complete rienngan of the juubi maybe madara still hasn't found out the story maybe his son was already born and he couldn't contain the whole rienngan so he sealed the sharringan part in his son)
what if when the sage fought the juubi he didn't have the rienngan and by sealing it in himself he got it but it wasn't the same as the juubi's
and his son (who's descendant's were uchiha) got the sharringan part of the juubi
(if u ask why didn't the sage get the complete rienngan of the juubi maybe madara still hasn't found out the story maybe his son was already born and he couldn't contain the whole rienngan so he sealed the sharringan part in his son)