What you're missing is that when people say an area is "becoming increasingly Black" they usually are talking about it going from 0% to 5%, or from 5% to 10%. Parts of San Francisco (at least certain businesses) are moving towards 100% white. It's a fundamentally different phenomenon.
If you look at real numbers, the white population of San Francisco has been declining for at least for the last 22 years (up until 2012). It is possible that in the last 2 years it has stopped, or even grown a little but it was 41.7% in 2012, and it is likely still under 50%.
Detroit isn't like that because all the black people moved in, it's like that because all the white people moved out once black people started moving in.
Then why don't non-white people move in to SF, just like in Detroit?
Alright, enough with the wisecracks.
The people moving in during gentrification are rich or rather richer than the current residents. Just because the overwhelming majority happen to be white is a mere coincidence arising of multiple factors. These people are not really white/black/brown, their only true color is Green, like the dollar bills in their banks and pockets. The color of their skin is secondary.
With all the song and dance about loss of diversity, in any city or context, I see it as a green-ification, not a white-wash or any other racially motivated term. This is a class issue that is always conflated as a race issue, with the the same lame excuse: because, history.