If research is the opposite of teaching, how can profs do both well?

I don't quite see why it should be contradictory. Yes, teaching imparts already existing knowledge. But on the one hand, there are not only pure fundamental lectures, but also seminars and project courses, in which new procedures are often tested or evaluated together with the students. On the other hand, no professor exclusively teaches or does research. In addition, professors have the opportunity to apply for a sabbatical, during which they have time to focus on their research. At least at my university, it was also common for most lectures or courses to be taught by doctoral students or research assistants.