Swearing coarsens language.
I'm not really sure what you mean. Are you saying that swearing 'makes what you say rude'? My opinion is that being disrespectful or insulting to somebody is rude, but using a word, whose literal meaning is sexual or refers to bodily functions, for added emphasis, is not.
Its purpose is to be grating rather than to smoothen and thus its nature is discord rather than harmony.
Even if this were true, there are times when I want my words to be harmonious, and there are times when I want them to be discordant. Language, by its nature, is required to effectively cover both. Swearing adds an extra layer of options.
Shakespeare loaded his writings with swear words. You might not recognise all of them as swear words, as such perceptions will always change over time, but you would at least recognise the blasphemous phrases, of which there are many.
How do you teach your kids to swear?
I will when they're old enough. As long as there are still people offended by swear words, I don't want my kids using them in situations where they're considered by such people to be inappropriate. I don't want my kids to go around upsetting people, even if I don't believe these people should get upset about it. When they reach the point where they can judge when and when not to swear, then I'll happily swear in front of them, and I'll be happy for them to swear in front of me.
As someone rightly pointed out earlier in the thread, one thing I will make very clear to my kids is that, if you overuse swear words, you totally devalue them, and by default, devalue what you are saying. I also don't like hearing people curse every other word, not because I'm offended by the words, but because it's an unimaginative and poor use of language.