If public schools stopped at those lessons, you’d have a point. Unfortunately, too many do teach values—the subversive kind.
Also, if a homeschool parent relies solely on his/her knowledge of a subject IOT teach, then that parent will fail. There are many, MANY terrific resources to draw upon that can teach your child beyond your expertise in a given field.
IMO, publics schools’ PRIMARY PURPOSE today is to teach values, to indoctrinate children into the leftist worldview.
This was one of the goals of the communists from the 50’s.
Take over the education system. And they have.
I continue to be amazed by the writings of people whose thinking is “pre-internet”. You can get access to practically EVERYTHING on the internet. If you really wanted your son or daughter to learn a foreign language at home, say German, all you have to do is get an online language course, listen to German radio online, watch German TV shows online (they have great kids shows with no leftist indoctrination), podcasts, online chat...etc! My biggest problem is having to sit in front of the computer for too long, but printers are also fashionable these days!
Moral relativism or more accurately, immorality, atheism, secularism, homosexualism, feminism and so on are larded and woven throughout all subjects in public schools. I home schooled my kids for some years, and tutored many other children, and read school books (not for some years) and often just made up my own lessons, the kids read library books (carefully selected, this was in the 80s). The most recent grade school text books I’ve seen were about 8 years ago. Even I was shocked at the blatant propaganda.