Letting your child "pick what they want to major in" sounds great in the shower, but I'm not sure it's a sure-bet strategy for all. If your child is extremely focused / determined and clearly knows what he/she wants to do, that approach may work, but how many kids in HS really know that? Additionally, for some of us who don't have excess cash, we need to make sure that there is a Return on Investment for the money we spend on our children's education since a)we don't have the money to pay for additional education if they made a mistake and need to change majors, b)we don't want to encourage the child to move back home because they've chosen a major with limited job opportunities and/or limited pay, and c)we want to see our children make a buck = we hate to see them struggle.
For these reasons we took a different approach = we looked at what they were good at and then guided them in a direction which matched those skill-sets.
All of our children were good a math / science so we asked them what they wanted to do. They told us "we don't know" and so we suggested they start-out in engineering and they could always consider switching majors later if they found something they really liked more. (Being an engineer I also knew that engineering grads usually had a better chance at employment than many other degress + you wouldn't starve).
As I wrote in the past above:
Son #1: Started in Chemical Engineering at Virginia Tech, left after a year and transferred to the University of Maine graduating in BioChemical engineering. Has a good job in the paper industry.
Daughter: Started in Biological Engineering at Pitt but quickly changed to Industrial Engineering. In her junior year she advised us that "I don't want to be an engineer"; we asked her if she wanted to change majors and spend another year or two in school...she said "nah, I'm this close now...I'll just finish up in Engineering". She graduated as an Industrial Engineer but went immediately into teaching (math), loves it, and she is convinced that her engineering degree got her into the very-competitive NYC Teaching Fellows program (which paid 100% of her Masters degree at Pace).
Son #2: Started in Mech. Engr, screwed around too much, we pulled in him out of school and he took 2 years off being a ski instructor, tending bar, and giving us heartburn as we hoped that, one day, he would go back to school. He has just started back at Buffalo...a little older, a little more mature, and we think he is on his way to finishing up there in 1.5 years with a Mech. Eng. degree.
Anyway, it has worked out well for our children with their math / science backgrounds and degrees but they have many friends who were just as bright but, instead, majored in marketing, business, etc in their respective colleges...and unfortunately it has not been as easy for them. The economy and/or the competition for the few jobs available has made life much more difficult for them; many are unemployed or under-employed. My point is, I think that, as parents, doing your best to guide your children into a field that offers a few more opportunities and/or pays a little better is not a bad decision. I simply don't think that most HS children are able to make that choice completely on their own...yet this choice can have huge ramifications down the road in terms of their employment opportunity and/or their earning potential.