a new teaching
In the synagogue in Capernaum, Jesus taught his hearers as One Who had authority, not as the teachers of the Law (Mark 1:22). And then, as if to authenticate His Teaching, Jesus cast a demon out of one who was present with Him. The people were amazed and remarked that this was a new teaching -- with authority, He even gives orders to impure spirits, and they obey Him (Mark 1:17).
We're told in many places in the Scriptures to beware of any "new teaching" that doesn't correspond well with the totality of God's Word, with the faith [that] was once for all delivered to the saints (Jude 1:3). Paul encourages us not to be blown here and there by every fresh wind of doctrine, but rather to be built up until we all reach unity in the faith and in the knowledge of the Son of God (Ephesians 13-14). Jesus warns us that, in these last days, false messiahs and false prophets will appear and perform great signs and wonders to deceive, if possible, even the elect (Matthew 24:24).
So then, isn't the teaching of Jesus suspect because it departs from the faith once delivered to the saints of the Old Covenant? In a word, "no". The Word of God in both Testaments is clear and without error in what it teaches, and yet it describes some additional customs and teachings that accrued over the centuries and obscured the true meaning of The Word. Jesus came to remove those overlays, not to abolish the Law, but to fulfill it (Matthew 5:17), much like someone who restores ancient art by removing centuries of grime.
So let's be diligent in recognizing fresh doctrine that is not aligned with God or His Word (and there's plenty of it these days!). Let's not be deceived by those who dazzle with words and wonders. But let's also embrace the refreshing teaching of our Lord, which has the power to destroy false strongholds and transform lives.