@eiholi -
Actually, my kids went to fairly ordinary public high schools – both went to public magnets but neither went to an academic magnet. They each had a mix of good, middling, and bad teachers. My son was the first NM semi-finalist that either his school principal or guidance counselor could remember in the years they had been there (significant because neither had a clue as to what they were required to do to help my son advance to the next stage, which involves submission of paperwork with a deadline.) My daughter went to an arts magnet - amazing for her chosen art (dance), but very weak on math and science.
My point was that the quality of teaching probably depends more on individual teachers than anything else, and you will find good teachers and bad ones at all schools, at all levels of education.
Obviously there are some elite private high schools that are well known for their academics and have a very strong commitment to assuring a high quality education for their students-- but there are also elite public magnets that fit the same profile. I didn’t have money on the private end, and I didn’t want my kids in high-stress environments on the public end – hence my decision to focus more on other factors than choosing a high school.