The way I explained it to my young cousin was like this:
Back before cameras, paintings were just recording reality, and that's why painters tried to be as realistic as they could, and only paint things that could exist in the world around them--objects, and people, and animals. Sometimes they did paint things from their imagination, but only to illustrate stories, like stories from their religion.
Then, cameras came along, and painters were free to paint things cameras couldn't see--things like the artist's feelings, or ideas, or thoughts, or lots of things. Some artists tried to see if they could paint from every angle at once, and we call that Cubism. Some artists tried to paint very quickly, as quickly as they could, so they could capture one single moment of the daylight, or their impression of a moment, with all the feelings light gives, and that's why we call them Impressionists. Some artists were more interested in the process of painting, like Mr Rothko; or in finding the most intense versions of a colour, like Mr Klein. Some were more interested in the spaces between things, like Mr Mondrian. But art, after cameras, could suddenly SAY something, say something by itself! And art, as it turns out, has a lot to say!
"I can do that too! I can do that!" You can, little friend! We all can!
My little cousin didn't get mad looking at modern art; she was excited, and asked her parents if she could have fancy grown-up paints, because she didn't know Art could be something she could do, could be something about expressing her feelings and ideas. This is a child who can't yet write very well, and not nearly as fast or as well as she speaks, so you have to understand something clicked for her, that she could express the complex human things inside herself with colour and shapes and images, instead of struggling to learn how to spell "melancholy" or "excited" or conjugate verbs to a degree that could encompass it.
Because words take TIME to master as an art form--I should know, I've been practising using them to express MY ideas and feelings artistically for 36-and-a-half years! Paint, however, doesn't require such mastery in order to begin expressing the artist; certainly it helps to know skills, but it isn't as required as it is with words. You can just scream and yell with paint, you can experiment more purely with images than with sounds, which after all are regimented into languages before we can begin to use them at all, let alone for the art words make.
And honestly, why are whole-ass adults not understanding that "I could make that!" should be exciting, should inspire you to go and make that! Why are you so mad? "I could make that!" Yes you can! And you get to! And you're an adult, you don't have to ask your parents to buy you paint and canvas and brushes, you can go and do that yourself and be expressing your own feelings this very afternoon! Nothing is stopping you! You don't NEED that plagiarism machine, you can do better art yourself! And nobody else in the whole world, now or in the past or in the future, is EVER going to be able to make the art YOU can make, the art YOU have inside you! So go make it!