Should we teach general relativity in high school? Why and how?

We discuss the proposal of teaching General Relativity and its spin-offs (black holes, gravitational waves, cosmology) as a part of the High-School curriculum, a task already undertaken by a few countries. We point out the importance of this proposal for the students and some possible reasons for the resistance of educators and scientists. A suggestion about how to circumvent the well-known mathematical and conceptual difficulties associated with this formidable task is made. It is not enough to stay at a qualitative level of explanation for High School students, although it would be desirable and positive at younger ages.