As far i am concerned, cartoon is not only meant for kids but also for adults. And another thing i have come to discover about cartoon as an avid lover of it is that, it's not only meant to entertain the viewers but to educate and enlighten the mind too, that is if taken seriously when watching it. Cartoon can never be said to be created for kids alone.
As for your case, you have to convince your parents that cartoon has essential cognitive benefits for adults apart from it be seen as children's mainstay movies or television programs.
You can also do more by taking the conviction a notch further with your parents by proving to them how watching cartoon has helped you improved your knowledge, as well as your vocabulary through your actions on a daily basis.