But if you do not believe his [Moses'] writings, how will you believe My words? John 5:47
Jesus called the religious leaders out when they fell back to their favorite defense – Moses. They were Moses' disciples. Followed Moses' law and Moses' traditions to the letter. They missed an important detail, though. Moses wasn't God. They followed Moses at the expense of following God.
Moses never intended to make disciples for himself, and if you read Deuteronomy, you get an idea how well Moses understood these people. The summary/paraphrase is "I'm gonna tell you all this stuff but you won't listen and God's gonna judge you. Then there will be a Prophet, but you won't listen to Him either."
If the religious leaders had been the great students and followers of Moses that they claimed to be, they would have realized who Jesus was immediately. They wanted to pick and choose which of God's messages they would believe, and then forget all the rest. We can't cherry-pick Scripture either. God's word is a unified whole, a revelation of one continuous story of God's redemption of His people.
If we discount some of it, then how can we can rely on any of it?