First, let me say I am not a Buddhist, I do study and try and practice it along with other things in life, but I am by no means devout. That said, when sitting back to watch Inside Out, I was prepared to watch and understand a lot about Psychology, which was heavily discussed around the movie prior and post its release. However, I found there was an obvious message the Buddha himself would of greatly appreciated.
No I am going to warn you, after this, this whole article is spoilers, so be careful.
Joy, We meet joy as Riley's first emotion as a newborn baby, with sadness right next in line. I cannot say how well put that was, that Joy and Sadness being opposites should exist next to each other from the beginning. Buddhism, I think, would completely agree with this, that these two are the two biggest and important emotions that drive modern humans, and they are opposites. The pursuit of pleasure (Joy), and the avoidance to almost detrimental terms of pain (Sadness).
So lets move on, in this, the whole movie revolves around Riley moving with her parents at Age 11. When she moves from her comfortable life in Minnesota, to San Francisco, all her emotions go into alarm, including Fear, Disgust and Anger.
Joy, in attempt to cling to her near perfect record of keeping Joy in Riley's life and keep Sadness away ends up creating more conflict and getting herself and Sadness booted to the remote part of the brain. Fear, Anger and Disgust are left to pick up the pieces, and they do horribly, as they do for anyone ruled by them in their lives.
With only Fear, Anger and Disgust to guide her, she makes a lot of mistakes. From pushing away old friends, pushing away family, and in the end trying to run away to be happy like she was before. Yep, more clinging. The clinging to pleasure, joy, happiness, what ever you call is it is a central part of Buddhism.
Clinging to pleasure (which the emotion Joy is utterly obsessed with) can much pain in our lives, as persistent pleasure is impossible. Sadness, Fear, Anger, even Disgust get their day too. When we avoid them, push them pack, they will come into play someday, and we need to know how to handle that.
The concept is very simple, and the way it works in the movie I would say is near perfect for how Buddha himself would of seen it.
In the end. Joy realizes that part of Sadness is empathy. Something we all need, that Riley desperately needed. That her holding back emotions only created more pain for her, but for those around her. Yep! and that many moments in our lives will be mixed, there will be Fear and Anger, there will be Joy and Sadness, that's part of life, and that we have to let it all in, accept it, bring it in, hug it, own up to it, and move on. In the end, allowing these emotions to have their time, enriches her so much, that instead of 5 personality islands, she has many more, which means a richer, deeper personality able to weather the hard times better.
So, yes, there is a heap of Psychology in the movie, but I would say there is a dose of Buddha's teachings in there as well.
Have a good one, and be at ease!