In the textbook, it goes over calculating double-sided and single-sided voltage gains and then states that only one output is available for real-world use but does not state why. Does anyone know the reason?

https://imgur.com/fCiGpfU

 

You can buy differential input and output amplifiers. They are often used as buffers for high speed differential input ADCs.
Most have a single-ended output because most applications only want/need a single-ended signal from the differential input, such as most op amps.

 

In the textbook, it goes over calculating double-sided and single-sided voltage gains and then states that only one output is available for real-world use but does not state why. Does anyone know the reason?

https://imgur.com/fCiGpfU

Actually, both sides are available, and produce signals of equal magnitude but 180° out of phase.

Some multistage diffi-amps use both legs as outputs to drive the next stage.

Ultimately, a single output signal must be generated -- and this would be taken from one leg.

 

Here's a whole page full of amplifiers with differential inputs and differential outputs. These are commonly known as "fully-differential amplifiers."