You're awfully quick to insult aren't you? Regardless of that, it wasn't selective reading and I was aware that you said that. You are also stating theories as facts now, which is not a good way to go in a debate. Based of the actual facts, we don't know if Hagoromo was born with the Rinnegan, if he awaken it before his battle with the Juubi or if he awaken it some time after becoming its Jin. Meaning that the Rinnegan may originate from the Juubi, and he may originate from Hagoromo's lineage. ( Or perhaps both ) Now, I'll just go ahead and skip over that second insult and go straight to the last point you pointed out. I don't "believe" that Pre-Jin Hagoromo is equal in battle strength as the current Madara. I believe in the possibility that he is, based of manga facts on how a Bijuu works.
I don't need proof, because what the manga presented to me already relayed that conclusion. Hagoromo's power comes directly from the Juubi, right when he was born. He also became its Jinchuriki, and gained more of its chakra. All his power is from the Juubi in one way or another. And what was an aspect of his power? The Rinnegan. It comes from the Juubi, whether you believe it or not is up to you. And his "lineage" is from his mother who also had the power of the Juubi within her, subsequently passing it on to him, as I previously noted. I apologize for the insults. I was rather quick to insult you.