There is accuracy and then there is practicality when it come to naming languages and variations.
When installing a spell-checker, they ask you is you want American "English" or UK "English"...or even Australian "English".
This type of distinction is common. You can argue with it, but there are reasons for employing it.

   I have always referred to myself as an English speaker. I know very few people who would say they speak "American". American is used as an adjective to name other things, usually.

If asked, I would admit that MY form of English is derivative and altered in many ways.....but many of the variants spoken IN England are also.