In many children's stories and TV shows, a kid will get into a fight with their friends, storm off, and then try to play catch, tether ball, checkers or some other game that requires a partner by themself to show that a person can't have fun alone. As a child, I used to hate having the message pushed on me that you can't have fun by yourself. I loved playing by myself as a kid, and I still love doing things alone now. Why play catch by yourself when there are so many activities that are actually more fun to do alone?
Children's media is primarily aimed at extroverted children and it confuses friendship with the false idea that you need other people to have fun. I love my friends and really miss them when I can't see them, but I miss them as individuals, rather than missing the "hanging out with friends" experience. Missing my friends doesn't mean that I have nothing fun to do by myself. When the media shows kids playing catch by themselves, they confuse the idea of missing an individual with the idea that it is impossible to have fun on your own. If a story is about a fight between friends, the friends could still miss each other, but not act like they have nothing else to do.
If a bunch of kids are playing a game that one kid doesn't want to play, the story shows the kid's failed attempts at trying to have fun alone, and ends by indicating that it's more fun to play a game you don't like with your friends than to be by yourself. But that's just not true for everyone - maybe it is for some kids who are really extroverted and just can't have fun alone, but those of us who enjoy playing alone in the first place can actually have a lot more fun doing something we love alone than doing something we don't like with someone else. If you want to address the friendship issue, the kids could take turns deciding what to play, or they could decide that in this particular instance, spending time with friends is more important than the activity. There are many different ways to get a lesson or message across, and there is no reason to diminish the value of having fun alone in order to prove the value of friendship. There's no reason to play catch alone.