![headscratch.gif](http://www.narusaku.com/style_emoticons/default/headscratch.gif)
I think that the Byakugan came from the Sharingan, but the Sharingan rose at the same time of the Rinnegan. It is possible that the Sharingan became active when the two brothers fought each other. The tomoes on the older brother may have activated, while the Rinnegan may have activated in the younger brother, allowing him to use Izanagi without risk.