Why use escribo intead of escribe?
escribo means "I write", whereas escribe means "he/she writes" or "you (formal) write".
Why cant you say "yo soy escribo"?
That would be something like "I am I write".
You use soy when talking about something that you are. For example, you could say Yo soy muy inteligente. That means "I am very intelligent". If you were to say Yo soy escribo, you would be saying "I am I write".
Yo soy muy inteligente
Yo soy escribo