Why did Arwen do that??

[The Saucepan Man]

I think that the key to understand Arwen's behaviour after Aragorn's death is in the quote provided by X Phial

How so? The quote is relevant to her choice of mortality over immortality, but I don't see how it is relevant to her choice to depart Middle-earth following Aragron's death. Once she had chosen mortality, her fate was joined with that of Aragorn, and their paths would lead together beyond the confines of the world, whether she departed following his death or whether she chose to stay in Middle-earth for the remainder of her natural lifespan.