Ease of Use
Although the refracting telescope is an older design than the reflecting telescope, the reflecting telescope is a simpler, easier to approach design. It is favored by those new to astronomy because its mirrors can be quickly calibrated if they become misaligned, but a refractor's permanently aligned lenses must be repaired by a trained technician should they move out of place. In addition, an entry level reflecting telescope offers more in the way of magnification than an entry level refracting telescope.
Cost
Compared with refracting scopes, a reflective telescope is inexpensive to manufacture. The reason for this is that reflective telescopes use mirrors, while refracting telescopes use lenses. These lenses must be made to exact specifications, and they are of varying thicknesses. Such lenses are much more expensive to produce. Likewise, a manufacturer can produce large mirrors more readily than it can produce large lenses. Therefore, more inexpensive reflective telescopes are on the market than there are refracting scopes.
Greater Magnification
The classic Newtonian design, the most popular type of reflecting telescope, is much more suited to astronomical observation than any refracting telescope. A telescope's magnification power comes from its length and its radius. It is very difficult and expensive to make a refracting telescope that is as wide and as long as many reflecting telescopes are. Therefore, if you are wanting a telescope to look at the heavens with, you would be much happier with the reflecting telescope. The refracting scope is much better suited to viewing Earth-bound objects from a distance.
No Chromatic Aberration
Refracting telescopes bend light through their lenses to magnify an image. As they do so, they bend the light to different degrees. This uneven bending causes a phenomenon known as "chromatic aberration." Chromatic aberration causes an object such as a planet or moon to be in focus in some areas and out of focus in others. You cannot encounter this aberration when using a reflecting telescope because its mirrors only concentrate incoming light, they do not bend it.