Symbols are context sensitive. If you look in Rev 12:9 you see "And the great dragon was cast out, that old serpent, called the Devil, and Satan,...", so you can't go about saying that every instance of a serpent is a symbol for Christ. Likewise in Isa 14:12 "How art thou fallen from heaven, O Lucifer, son of the morning! " and Luke 10:18 "And he said unto them, I beheld Satan as lightning fall from heaven"
You are of course free to disagree and hold your own opinion if you wish. It is not our custom to 'prove' anything by relying on man's wisdom, instead we explain our faith and encourage others to pray and find out from God if it is true or not. God's answers are proof enough for those who love Him.
How then do you justify calling Satan by the name of Lucifer? There is no context to prove that but there is context to prove Lucifer was the personification of the king of Babylon. In the case of the serpent, as Moses lifted up the brazen serpent on a pole so would the Son of man be lifted up. What is the connection in your mind?