1) You deal with whiny pilots....
2) You deal with whiny flight attendants....
Oftentimes when you meet them out on the road they will inevitably 1) whine about something and then 2) ask you how you deal with so many whiners. I met a captain a few months ago who wanted to know why he was rerouted . . . in 2002.
In reality, if having to deal with complainers or whiners is going to keep you out of a job, you'll be unemployed for life. Professionals learn to deal with those sorts of things, although too much of it can break a good culture down.
I reread my post above and thought of a few more things, so I thought I would add them.
The people aspect is huge. Schedulers hear from Pilots who need to be replaced because their wife just gave birth, their son is in the hospital, a family member just passed away, etc. You see every slice of life and you get to lend them a hand when they need it most. I took a call once from an FO whose father had passed away; he was standing in a jetway when he got the news. Thirty seconds later he's on the phone with me - that can be a heavy experience for some people, but it's also an opportunity to serve others when they need it. We get cards quite frequently from Pilots thanking us for helping get them home when some life event happened unexpectedly. Most of our reserves commute and it was common to release a guy on his last day and give him a few ways to commute home, on us or offline.
It's a great place to start your career in aviation, especially if you do not have very much aviation background. I fit that mold when I started with my company; I had traveled the world and thought airplanes were awesome but I didn't go to an aviation college or work the line at an FBO as a teenager. In some ways it can give you the benefits of an internship; if you work hard, pay attention, and take advantage of opportunities you will see how an airline works. In my first few months I was fortunate enough to see a little bit of Training, Dispatch, Maintenance, Ground Ops, Flight Ops, ATC, Customer Service, and our in-house Technology group. The experience you gain working in Scheduling will help as you move about in the company.
And, since this is a Dispatch forum, I will add that Crew Scheduling is one of the best ways to get into Dispatch.