Not a true statement, but whatever gets you through the day.
Sure there may be a larger quantity of kids that go from private - but it isn't the be all and end all.
Plenty of great players come out of public school - girls and boys - that go on to play at all different levels.(yes, DI included)
13% of all high school lacrosse players go on to play lacrosse in college (all 3 levels). If your kid is part of that 13% at any level - from public or private - then be proud.
Division 1 is awesome; however, there is often more money at Division 2, and Division 3 schools are nothing to scoff at - there are more opportunities to play (3x the number of DI schools). Playing a sport in college is admirable at any level and there are lots of options out there. If the message to your kid is that DI is the only goal and the only option for a great player... then you aren't well informed.