In The Outsiders, why does Ponyboy decide to write his English paper on his life as a Greaser?

I believe Ponyboy decides to present himself as a greaser simply because society perceives him as one; he is often criticized for not having proper manners or not being gentleman enough, which is why he is seen as an outsider or as a greaser. He doesn't like the fact that the society judges him by his appearance and sees him as an uneducated and violent person; however, he realizes that he can't do much to change how other people see him, especially because he grew up poor and in a lower-class family. Thus, he decides to embrace his greaser image.
I think that Ponyboy was inspired by his realization that even the smartest and most well-mannered person can be seen as a greaser if he/she was poor or came from a broken family. This is why he decides to write his story not as something personal, but as something that all people who are seen as outcasts and greasers can relate to; his main reason was to provide comfort for the greasers and make them see that they are as good and as valuable as everyone else; he also wrote the story for the socs and the rest of the society, so that they can see that they are judgmental and unfair. Essentially, Ponyboy hoped to change the situation and make everyone treat each other equally and with kindness and respect.

In the last chapter of the novel, Ponyboy reads Johnny's letter encouraging him to tell Dally about sunsets, explaining Robert Frost's poem, making peace with his unfortunate situation, and urging Ponyboy to cherish his innocence. After Pony reads Johnny's moving poem, he immediately begins thinking about the hundreds of other boys in similar situations, who live on the streets and are negatively affected by senseless violence. Ponyboy suddenly realizes that he may not have the opportunity to help Dally anymore but can positively impact the lives of other adolescent boys living difficult lives. Ponyboy says,

It was too vast a problem to be just a personal thing. There should be some help, someone should tell them before it was too late (Hinton, 152).

Ponyboy then calls up his English teacher, Mr. Syme, and asks him how long his theme assignment has to be, before he begins writing about his experience as a Greaser. Overall, Ponyboy decides to write his English paper about his life as a Greaser in hopes of positively affecting those adolescents living difficult lives on the streets. He also wishes to provide fortunate adolescents with an in-depth look into the lives of their lower-class peers in hopes of helping them develop sympathy for less fortunate people.