Correct, it just gets call "indoctrination" as that sounds nicer and it is often (though far from always) more subtle as it is more of a "long game" thing.

It is one of those "one person's X is another person's Y" comparisons: indoctrination/brain-washing, religion/cult, freedom-fighter/terrorist, cute cat / insane evil sharp edged ball of allergens, ...

No, the nicer sounding word is "explanation".

I don't agree there. Explanation would be more "I do/think/believe X because" where indoctrination is more "you should do/think/believe X because".

A more passive form of indoctrination would be repeated explanation (with or without query/prompt) so explanation can become indoctrination depending on context, but I'll stand by my choice of words above.

Your examples answer the wrong question.

"Where do rainbows come from" can be answered with the explanation "As a way to show God's promise to Noah never to flood the Earth again" or with the explanation "because sunlight refracts through water into all the different colors we can see" or with the explanation "invisible unicorns fly through the sky sometimes and leave rainbows where they've gone".

Many people would call one or more of these indoctrinations, despite the complete lack of "should" in any of the responses. Egocentrism does not a benignity make.

I don't know if you are being facetious or not, but I think all religious teachings for children count as brainwashing.

Alao if the religious beliefs are agnosticism? Basically, by this definition, all parenting is brainwashing.

no, no, no, if you teach your children beliefs I approve of, that's different...

Not if you teach your children critical thinking and to base their opinions on something provable.

Then you're still doing brainwashing/indoctrination. Let's not forget, it's "irrespective of the opinion's merit".

Besides, just as you hold your "must be provable" views dear, similarly the religious parent holds his or her religious views dear.

I think there's a useful distinction between teaching a set of opinions that must be held regardless of evidence and teaching the practice of forming one's own opinions based upon evidence, but it's a tricky point to make.

I would say that the oposite is true. Brainwashing takes the same mecha isms that we use as humans to be able to learn our how to behave in the society, and how to learn to be a person. I have small kids and they are like empty disks looking for something to copy. They copy behaviours that sourround them and make them part of their personality.

Adults just slow down the writting but we always try to fit in the social group that we are living. And that includes political opinions, faith, etc...