On top of all that, the indoctrination is nowhere near guaranteed to set in. Anecdotal TMI example, my parents are bluefash libtards whose homeschool curriculum included what was more or less critical race theory. I turned into a total chud so it clearly doesn’t always apply permanently
Wokeness cannot take hold in a mind capable of genuine critical thinking. This means your parents likely did a better job teaching you how to
think than a public school would have (which is really the biggest reason home schooling is such a threat to the state's education systems). Public schools don't teach people how to think critically. They're taught instead that asking too many questions leads to punishment and ostracization. Meanwhile, even though your parents probably
mandated "thou shalt believe these specific things like we do," they also taught you to ask the world's most useful question: "why?" and to be satisfied with answers you reach even if they disagree with what they've "ordered" you to think.
A better example might be this: public schools teach arithmetic via rote memorization ("memorize your times tables!"). They expect you to learn "1+1=2" and "2+2=4" because they say so. They never once stop and just ask you "say, y'know how 1 plus 1 equals 2? Ever thought about
why that is?" They expect you to memorize, well, the multiplication tables, instead of asking "why does 3 times 4 equal 12?"
Those aren't hard questions to answer. "Why does one plus one equal two?" Take an object (just one), and put it on a table. That's one operand. Take another object (just one) and put it on the same table. That's the other operand. Put them close together. That's the operator. Count them. Oh hey neat, you have two now. 1+1=2. Addition is "counting" in your head (or on paper) without actually using physical objects on a table. Addition
builds on counting. If you can count, you can add.
"Why does 3 times 4 equal 12?" Start at zero. Now take the number 3, and add it to your total. Do that four times. You start at zero. Adding 3 to it one time gives 3. Adding 3 to zero two times gives 6. Adding 3 to zero three times gives 9. And finally, adding 3 to zero four times gives 12. You are adding the same number to itself a specific number of times. That is, you're adding
and counting -- both concepts which multiplication builds upon. If you can count and add, you can multiply.
Subtraction and division are similar (subtraction amounts to "counting backwards" and division amounts to "counting after splitting."
Learning to count to ten is literally the only "memorization" you need to start learning mathematics. Literally just learning the names of the digits and which order they go in. Everything else can be acquired by intuition and guidance.
Public schools don't teach any of that. They present single-digit result tables as things to memorize, and then teach multiple-digit operations based on memorizing those tables instead of "reasoning." It technically "works," but with no concrete foundation about what's going on, most students struggle once you get past simple arithmetic into beginning algebra (around the time you hit somebody with PEMDAS, they're more likely to be completely lost if they don't have any understanding of
how those operations work). It's just memorization stacked upon memorization and it becomes a house of cards because there's no foundation.
Incidentally, a child who figures out (or notices) these concepts on their own (or with just a bit of prodding) and takes to it is very likely to be a
very competent mathematician if encouraged to do so (and if they actually enjoy it).