I believe (based on my experience passing through this stage) that is does matter. In fact, I think it matters which high school you go to because it makes a difference which college you can get into. Education is one area where you should try to go to the best place you can - it will make a difference one day. Now there are tiers - if you go to a high caliber school like U Berkeley versus Stanford - it probably won't make a huge impact. But if you go to U of Houston versus Berkeley or Stanford - you get the point.