I don't think that proves Jesus was a Pharisee. You have to look at the whole picture. He doesn't fit into any single group. Yes, crucifixion was a Roman thing. But Jews did believe in the death penalty then and would most certainly believe anyone who claimed to be God deserving of it.
the only group he fits is PHARISEE---WHOLE PICTURE. As to death penalty---NOPE----at no point does Jesus CLAIM TO BE "GOD" ---Even making the major
leap that information one can glean from the NT is factual----the actual reality is
that the enemies of Jesus were THE ROMANS and their SHILLS---Herod and
Caiaphas. The claim that Jesus was a "threat" to the Pharisees is ludicrous. The claim that they wielded the POWER is also ludicrous. Your sunday school teacher
transmitted ROMAN INFORMATION to you because the ROMANS hated the
Pharisees and still do. An anecdote----long ago whilst wandering around the hospital
in which I then worked, I noticed a patient reading the works of Josephus Flavius. The man wore a crucifix and had a rosary tied to his bedrails. Days later I noticed
that he had abandoned his book and had been discharged. I picked it up and read the forward written by a catholic clergyman. It praised the book EXCEPT for its ONE MISTAKE----the ONE MISTAKE is that Josephus had FAR TOO HIGH OPINION OF THE PHARISEES. THE BIG MISTAKE OF JOSEPHUS. -------for me---the joke
of the day-----reminded me of conversations I had in my undergraduate days with
a divinity student from Seton Hall. That would be priest was just as brainwashed
and ill informed as are you.