If we hear teaching with authority, there are a number of ways in which that authority might function.
The sense of authority in the teaching might be by virtue of the identity or position of the teacher. It might be the critical mass of the group who’s attention the teacher commands. It may be the teacher’s qualifications, experience and expertise in a given field.
Jesus’ teaching with authority addressed the heart of his audience. He managed to activate an innate sense of what is true and what is in accordance with love. Then he called for a response.
He called people to follow him as he lived his teaching in front of them.