...
So just because you have Jesus debate with other Pharisees doesn't mean
that Jesus rejected the Oral Law, nor does it mean that Jesus wasn't a
Pharisee Himself. ...
Indeed. But if you read the gospels, which are (as James pointed out)
more or less the only records we have of the historical Jesus, we find
that Jesus rarely debated with the Pharisees, but more frequently he
simply condemned them - and vice versa. For example, see the repeated
"Woe to you, teachers of the law and Pharisees, you hypocrites!" of
Matthew 23. Note that he doesn't say "Pharisees of that other school",
he addresses all Pharisees, and all teachers of the law. It is clear
that he is not counting himself as one of them, but as an outsider
challenging all of them. That doesn't mean that he disagreed with all of
them on every point. But it does make it impossible to claim that Jesus
was himself a Pharisee.
Earlier you mentioned verses 2-3 of the same chapter, where Jesus tells
people to be careful to do everything that these same teachers of the
law and Pharisees tell them to do; but in the light of what follows,
that can only be understood as ironic!