not a direct quote... excerpts somewhat rearranged, for clarity and direct comparison:

Current NYC District 15 Middle School Admissions:
Now, students rank the schools they want to attend, and schools rank students they want to enroll, based on varying criteria such as course grades, test scores, behavior, attendance, punctuality and auditions. The department makes matches.
...
Comments on Current NYC District 15 Middle School Admissions:
1) Michele Greenberg, a District 15 parent: “Children shouldn’t be rejected because they don’t somehow fit,”
2) Many parents complain this complex process brings massive anxiety, and often leaves disappointed children in tears.
3) 58% of 879 respondents considered it appropriate for middle schools to screen for admission this way. That included 62% of 321 respondents from "more-affluent" Park Slope, where Mayor Bill de Blasio lives, and 42% of 162 respondents from "low-income immigrant neighborhood" Sunset Park.
...
Proposed NYC District 15 Middle School Admissions:
Applicants for sixth-grade would rank their favorites. The department would
1) give priority for 52% of each school's slots to students who are poor, homeless or English-language learners.
2) try to give students their top picks,
3) offer seats by lottery to oversubscribed choices

A few questions which may crystallize the debate:

1) Does the proposed plan eliminate rejecting children who don't somehow "fit"?
To address Michele Greenberg's criticism of the current admissions criteria: Do you see that under the proposed plan, children are rejected because they don't somehow "fit" with priority demographics: poor, homeless or English-language learners?

2) What criteria creates a better match to a school's academic program, and the ability for that academic program to meet students' educational needs:
2a) selection based on course grades, test scores, behavior, attendance, punctuality and auditions...
2b) priority based on poor, homeless or English-language learners?

3) Which process better emulates "real life" for college admissions, job applications, and other opportunities such as internships, volunteerism, running for elected office... and provides feedback as to ability and readiness?

4) Will the proposed process NOT bring massive anxiety, and NOT leave disappointed children in tears?

5) The article reports that a majority of parents (58%) support the current middle-school admissions criteria.
- In a democratic system, wouldn't that majority prevail?
- Why take on the expense of re-tooling the middle school admissions process, not initiated by the taxpaying citizens... but dictated by the government?

6) Because the article mentions "low-income immigrant neighborhoods," how many of these residents are in NYC legally, how many are undocumented/illegal/overstayed (therefore have not paid to support the public system which is giving them top priority)?

A few thoughts:
1) Different students have different needs.
2) Grouping by ability and readiness to learn a particular subject and level is a researched, evidence-based, efficient way to meet student needs for appropriate academic challenge and intellectual peers.
3) Changing admissions criteria will necessitate changes in programming at each school, in an attempt to meet a broader range student needs, abilities, readiness.
4) There is an old adage: "What you reward, you get more of." Rewarding course grades, test scores, behavior, attendance, punctuality and auditions encourages students to do their best. Changing to a system which does not reward best effort and eliminates competition signals devaluing a work ethic. This seems likely to erode the American Dream of upward socioeconomic mobility... which is based largely on multi-generational hard work, sacrifice, and saving within families.