Reflectors are popular due to their superiority to large, lens based refractors. They also do not distort colors as refractors do- a phenomenon known as chromatic aberration.
Reflectors are popular among professional astronomers because they are cheaper and have no chromatic aberration. Amateurs often use refractors, or Maksutov-Cassegrain telescopes which have both mirrors and lenses.
The biggest reason is price. They are much cheaper than other types. They also offer wider range of vision. They are perfect to build as a science project.