You'll save money in the long term. Although the razor may be more expensive, replacement blades can be as cheap as $30 annually, compared to over $100 with the replacement cartridge.
You'll have the best and closest shaves of your life! Once you hone your shaving skill, you will have a better, closer shave. The razor blades are sharper and don't irritate your skin.
Reduce environmental impact. This ranges from less water used daily (don't need to run water constantly) to less material waste from the canned shaving creams. The single blades can be recycled. The razors themselves if taken care of can last a very, very long time!
Better for you!If you have "sensitive skin", I bet it's your razor. The multi blade gimmicks are rough on your skin as you have to apply more pressure to get a close shave. More pressure = more razor burns and ingrown hairs. The sharper single blade of a double edge or straight edge razor will cut more efficiently, therefore less pressure!