The Image Is No Light Matter
Refracting telescopes have an objective convex lens that resembles a teardrop and gathers light, which it then focuses on an eyepiece lens for viewing. That bends the light, distorting the image. Reflecting telescopes, on the other hand, gather light with a concave mirror, which appears to be scooped out with its rim higher than its center. The image that the mirror gathers is then reflected into an eyepiece lens -- but without the distortion of bending.
No Admiration for Aberration
Lenses on refracting telescopes bend different colors of light different ways, resulting in a blurring of the image known as chromatic aberration. Even the roundest lens is never perfectly round, distorting the image by spherical aberration. Astronomers tried to overcome those problems by grinding bigger and bigger lenses -- which weighed so much they caused the telescope tube to sag and, yes, created more image aberration. Reflecting telescopes' mirrors can be supported on their backs, not just their edges like refracting telescopes' lenses, which eliminates sag and allows development of mirrors hundreds of inches across.
Size Matters
The bigger the lens on a refracting telescope, the longer the tube you'll need. The history of astronomy is full of stories like that of Pennsylvania's John A. Brashear, who in the 19th century made a 5-inch refracting lens, which he fitted to a 9-foot-long telescope tube. To work the telescope, Brashear had to cut a hole in his roof. Reflecting telescopes can use multiple mirrors to bounce the light while shortening the barrel length, saving space and roof shingles.
Money Matters, Too
Lens grinding is as much art as science, and good lenses are expensive; a refracting telescope with the same image-gathering power as a reflecting telescope can cost hundreds of dollars more, as of May 2011. R.F. Royce, who builds telescope parts for a living, described refracting telescopes with lenses larger than 6 inches as "insanely expensive," especially compared with reflecting telescopes with mirrors of comparable or even larger size.