The law -- not my opinion, but the actual law -- is this: It's okay to have a giant Menorah on government property if there is a nativity scene on the same property. (By the way -- you made a general mention of a "hoorahrah" about crosses, but did not support your statement with reference to any source.) It's also okay to have a cross or a nativity scene on government property if other religions are also represented. The article you linked does NOT mention anywhere that there is no nativity scene at the White House. I am pretty sure there is one -- as well as a Christmas tree.
Please support your statement with a news source that states that there is no nativity scene or other Christmas attributes on White House property. In the event you can't document that, what exactly is the problem -- the fact that there is a menorah at all?
EDITED TO ASKER
You said: "Christmas trees aren't of Christian origin it's of pagan origin." Oh, do you REALLY want to go there? Methinks you don't. Not only Christmas trees are of pagan origin -- Christmas is of pagan origin. It does not coincide with the actual birth of Jesus and was instituted merely as a replacement for earlier pagan winter festivals, including Saturnalia (made early medieval pagans' transition into Christianity easier). None of the gospels identify a birth date for Jesus, but circumstantial evidence suggests spring or summer -- certainly not late December; and the reference to a census means the year of his birth was no later than 4 BC. Christmas has little to do with historical Jesus. So if IT is "Christian" enough, so is a Christmas tree.