Why is the 'present participle' not called 'continuous participle' if it uses ing?

Good question. The names given to things are arbitrary. The first people to write grammars of English, in the 1800s, used the terminology they had used to describe Latin. But English is not a Latin language, and the classifications don't always fit English.  What we call the present participle and past participle have no connection with time, and it's just very confusing that they are called that. I like your suggestion of "continuous participle"- or "progressive participle"- but you'd have to get all the grammar books and textbooks to change.