I'm curious where it's said that his use of the symbol came first and that it was then applied to Christianity. Genuinely interested in reading the source (not trying to be a d!ck).
The cross was a very interesting symbol for the Christians to use, it was, as Paul mentioned, a stumbling block for the Jews ( to be "hung on a tree" was a very bad death for a Jew) and to preach it was considered foolishness for the Gentiles ( Why preach that your lord and saviour died like a common criminal?), and yes, in Paul's own words he boasted in nothing but the Cross and Jesus cruscified on it.
Why?
The Gospel of john sheds some light on this:
"God so loved the world that he gave his only begotten son for it".
The cross is a symbol of God's eternal and undying love for Us, a love to strong that to show us this love, to prove to us that we are worthy of it, God ( God's essence) in the Flesh, died for Us.
Psalms 144:1
Praise be my Lord my Rock,
He trains my hands for war, my fingers for battle !