Another Sarah, that was an excellent post.
No one here has said that everyone must always shake hands, no exceptions, or they are rude. It is generally considered rude in western society to refuse to shake hands, but there are many exceptions, and one need only excuse oneself politely.
I find it troubling that some posters aren't content with the answer, "Don't shake hands if you have a problem with it, but find a polite way to do it that does not come across as a rejection of the other person, because shaking hands is indeed the social norm here."
Some people seem to argue that the norm itself is stupid or unsanitary, or isn't really a norm at all, or is unfair to people who have unusual mental or physical conditions or religious constraints, or doesn't count because there are other countries in the world where it isn't the norm, etc., etc., etc. -- so there is no need to apologize or otherwise mitigate any offense or misunderstanding, because any hard feelings are completely the fault of the other person, whose expectation that everyone must live up to "their idea of good manners" is what is unreasonable.
But whether we like it or not, it is indeed the norm, and it is considered good manners in western society to shake hands -- and, accordingly, extremely bad manners to spurn a handshake, so much so that any refusal to shake requires an immediate excuse and regrets.
Why is it so hard to do that -- apologize for not shaking and give a reason, true or little-white-lie, and some other sort of indication that you are indeed glad to meet them? Why is it necessary to go farther and insist that the social convention itself is wrong and not really a rule of etiquette at all? If you are forgiven a speeding ticket because it was an emergency, isn't that enough, or do you feel the need to further insist that the entire speed limit isn't really a rule, just "someone's idea of good driving"?
It should be enough to be excused from conforming, without condemning the rule itself or insisting that it doesn't really exist except in the minds of fussy, unreasonable people.