It's a very long story involving lawsuits over racial discrimination (an Asian-American parent wasn't happy Lowell, the academic high school, set racial quotas), that led to assignment formulas to try to get diversity without using race. The crazy matrix only made segregation worse and now the district has a whole other system starting this year that gives some weight to where you live. So if you live near Lincoln you have a slight advantage over an applicant from North Beach.
All in all, despite the stress and helplessness lots of parents feel with the lottery-style system, it gives everyone more choice. Instead of having to go to the neighborhood school you may not like, you can try to get in anywhere in the district. Now that there are interesting programs, such as language immersion programs, etc., lots of parents like that flexibility.
That said, the west side school requests are 200% of capacity. So the district still has a lot of work ahead of it to improve schools across the city.