You're not wrong. Any *schooling* that does more than teach kids reading, writing, math, and problem solving skills can be considered indoctrination.
The right certainly does it as much as the left.
The difference is they do it in private schools, whereas the left has co-opted public schools and universities.
The right, gullible as they are on some issues, seems to feel the best way to go about this is to make it legal to have vouchers and school choice, etc., while the left simply took over the schools with a ground roots effort in school boards, teachers unions, etc.
