Why is your sense of taste impaired when you only breathe through your mouth and not your nose?

Smell not taste. Taste is sensed through the mouth. Example is sweet. The flavor of food derives mostly from smell . The smell sensors are located in the nasal roof.
Smell Problem effect. The tongue can detect only sweet, salty, sour, and bitter tastes. Much of what is perceived as "taste" is actually smell. People who have taste problems often have a smell disorder that can make it hard to identify a food's flavor. Flavor is a combination of taste and smell. Taste problems can be caused by anything that interrupts the transfer of taste sensations to the brain, or by conditions.