The second sentence I don't agree with what you said. "I don't agree with what you said", the subject is me, the predicate is agree, the predicate.
Some disagree, some agree "agree ……", and the object part is the clause you said.
I don't choose am agree, because am is a be verb, usually followed by the ing form of a noun, adjective or verb.
As a predicate, this sentence already has the predicate agree.