Different conclusions are reached when one fact is viewed from two separate points of view. When that happens, there is no immediate way to judge which point of view is the correct one. There is no way to conclude one’s own conclusion is the correct one.
Re: why did they go to
TBH, I am think that since Hamura and Hagoromo were brothers if the Shikifujin was tied in to hamura it could be that Hamura set it up so that you would need his brother"s (Hagoromo's) chakra in order to undo the seal. The Uchiha Tablet was written by Hagoromo after all
It couldn't just be for privacy because Orochimaru called it the place where all the secrets lie, in other words it was some place important to their goal.