They aren't arguing that AAVE is another language entirely. They're arguing that it's a dialect of English. So not separate, then. Their point was that it's a lot easier to teach kids to read and write in Standard English if, at least initially, the teaching is done in AAVE. I think that you'll find consistency if you read more closely. For reference, Standard European Portuguese and Spanish usually aren't mutually intelligible, and are viewed as different languages. Different situation entirely. Portuguese and Galician might be a better comparison, maybe... But that's good for another conversation....But both list AAVE as a dialect of English. This is undoubtedly the right classification.
Journalists vied with each other to insist that AAVE should not be recognized as a language. What got lost was a much more reasonable and sensible point: AAVE as a dialect of English still deserves respect and acceptance.