Because it’s a movie aimed primarily as kids that has awesomely diverse female representation when it comes to personalities, as well as beautiful animation, explains minds and emotions and memories and all that stuff in a way children can easily understand, passes the Bechdel test in like the first ten minutes, and stresses the importance of your own personal mental and emotional health.
This is a movie with a female protagonist (who enjoys both rainbow unicorns and hockey) that tells kids that if they’re feeling out of sorts, if they’re feeling sad or angry or afraid or disgusted, that’s okay. That’s normal. And it’s telling them to speak up, to tell someone, to express what they feel, because bottling up your emotions - putting on a brave face when you really need to cry - only leads to more pain.
Inside Out teaches kids that it’s okay to feel and that is so, so, so important.