What influenced the early Catholic leaders to adopt such a perverse doctrine is really not important.   I suspect it was simply Carnal Minded thinking.   

There are three things wrong with the doctrine of the trinity.   
   ➛ it denies Jesus His singular glory
   ➛ it diminishes who the Holy Spirit is
   ➛ it creates a false being called the 'Father'

Jesus is the Spirit Soul And Body of the One and Only True And Living God.