Are your parents basing this on some ranking from a magazine? Those are based on arbitrary criteria. Depending on how you weight the criteria, you can end up with a different ranking. For example, if you rank by popularity or reputation, the top schools will be those with the most students and graduates and/or those who have spent the most on marketing. If you rank by selectivity, well, there are several schools that are far harder to be admitted to than Andover and Choate. If you rank by the percentage of graduates who end up at Ivy League schools, you have to consider that these East Coast boarding schools have more students who have a leg-up on Ivy admissions simply because they have relatives who attended, too. That doesn’t improve your own chances at all.
Please encourage your parents to speak to people knowledgeable about boarding schools and education instead of relying on rankings designed to attract eyeballs and sell ads.
Most boarding schools are in beautiful locations and have lovely facilities. That is NOT how one should choose a school 