I actually went to one of those specialized high schools in NYC.
I haven't looked into what DeBlasio wants to specifically change since I'm past high school
(I should look into it though), but I do agree the admission criteria should change.
Basically the criteria is one single exam you take in the 8th grade. It's a tough exam and you have to be smart to do well on it, no doubt. However, the issue with the process is that the majority of the students are coming from specific sets of middle schools. The middle schools with a high Asian population etc.
The issue with this is that minority students are attending middle schools/educational systems that aren't on par with the middle schools that feed a lot of the students into the specialized high school. They don't have the same opportunities because of where they live. They may live in a rough part of NY because of their family upbringing etc. None of this is in their control.
I'm assuming DeBlasio/other individuals sees this as a problem and wants to help these students enter into the specialized highschools so they finally have the opportunity to have a great education. And trust me the high school provides unparalleled education. The only thing that may be an issue is that the new criteria may allow students that can't handle the work load etc. However, these kids need to be afforded these opportunities to improve their situation.
Side note, I felt my high school was diverse. There could have been more minorities sure, but it was definitely more diverse than my university. I knew plenty of minority kids who were able to fight off a great deal of hardship to succeed in that high school as well. Those kids were special though, not everyone can do that.