Unless you yourself are suffering from a social disability, you should be able to come up with something that doesn’t make you feel uncomfortable, for Pete’s sake. Nobody expects you to reveal your private business or even tell the truth. You just use some of that social grease that makes ordinary interactions smoother.
This can’t seriously be a surprise to you. It’s ridiculous that I even have to say it.
My favourite example of this is a possibly apocriphal story concerning Queen Victoria.
Allegedly, in her diamond jubilee year she invited several Indian luminaries to a formal dinner at her palace. After the dinner, her guests were presented with finger-bowls containing water with lemon. The Indian dignitaries, unfamiliar with this custom, drank them, rather than dipping their fingers in them.
There was a gasp. Beads were clutched. Monocles fell from eyes.
But Queen Victoria, seeing this, raised her own finger bowl - and drank from it, too.
I’m not arguing, I’m informing. If you say only “no” in a case like this, you are being rude.
It can be acceptable, sure, in a case where you say it with sensitivity to the uncomfortable position you’ve put the interlocutor in.
You have already been given an example of a perfectly acceptable response that does not include an explanation: “Thanks for asking first! But not today, I’m sorry,” with a smile. Very polite, not curt, doesn’t make the child feel bad for asking, and doesn’t give an explanation for why not.
I’ve read etiquette guides on occasion as well and what the good ones have in common is an understanding that the underlying principle of etiquette is in being respectful of other people’s feelings. Rigidly applying a rule of etiquette just because it’s the rule, even though it makes you come across as a bit of a dick socially, is not polite in the slightest.
What!?!? That’s not cold lemon soup? Well that explains a lot of things.
I’m getting from all this that “Sorry, no” may not be impolite according to some formal rule of etiquette, but it seems to be clearly unfriendly.
I don’t know if you have a mother or if she’s still alive. Let’s say you do, for argument’s sake.
You’re feeling bummed out by something. You need a hug. You ask your mother for a hug, anticipating that she will say yes because she normally does.
In response to your inquiry, she says, “Sorry, no.”
How do you feel?
I’d feel my mother was being unusually polite. My parents were incredibly cold people.
I don’t see how that scenario applies at all to the case of a request from a stranger. Suppose you had one of those nice mother’s, who if you were bummed out wouldn’t explain to you why it was your own fault, and actually gave you hugs. Do you think you get the same response asking for a hug from a stranger.
No, because, in context, it’s not routine to ask strangers for a hug and expect a yes. However, it is routine to ask other things.
So have you figured out that this is bad thing yet?
I repeat with approval what was said above. People are free to allow others to think whatever they want. And the fact is that if you say “sorry, no” to a polite request which would usually recieve an affirmative response, people will think you are someone who doesn’t mind making others uncomfortable.
Asking to pet a dog is still not the same thing as asking your mother for a hug.
But in both cases, by refusing, you will cause someone to feel disappointed, and if you are sensative to that, and if you care whether the other person thinks you are the kind of person who doesn’t mind making others feel bad, you will add something to the “sorry, no” to alleviate the discomfort.
Well, no. Because I know that context matters. I wouldn’t expect to get the same response from the same question given a different person. My mind is not so rule-oriented.
A hand-shake is about as familiar as I’d like a stranger to get with me. A hand-shake is a sign of friendliness and respect. When people extend their hand, they usually expect it to be shaken. When I extend my hand, I usually expect it to be shaken.
If someone were to say, “Sorry, no” in response to me extending my hand, I would be confused and likely to blame myself (do I smell bad?) or think the person was a jerk. Chances are I would not think good things. The whole point of being polite is to avoid making people think bad things…whether they be inwardly or outwardly directed. If you don’t want to be polite, that’s fine. But you can’t insist that an ambiguous statement like “Sorry, no” is polite when it leaves so much room for discomfort. Especially when a couple of tacked-on words is all it takes to take that awkwardness away.
You can’t go wrong with an explanation, even a lame one. But you CAN go wrong with no explanation. The question is, what do you have to gain by taking that chance? Your dignity? Righteousness? Well, if maintaining your ego-boundaries is that huge, you shouldn’t really care if you come across as rude. People who don’t want to offend people don’t care about winning asinine imaginary battles.
Who said they have to be the same thing?
I remember one time someone I had just met offered to help me, and I politely said “thank you, but I can do it myself,” and I even smiled at her when denying her offer, and she never talked to me again for several months. I only denied her to save her the trouble. Bad idea.
Another time, I similarly turned down an offer of help, with a polite smile, and I was met with some sort of grunt or sound of disdain. I, again, genuinely thought that I was saving the other person from the trouble of helping me.
I now have to remind myself not to deny offers of assistance … doesn’t seem to have done me or anybody else any favors.
Did you literally say “Thank you, but I can do it myself?” If so, you made it sound like you were insulted by the offer.
“Thanks, I’m alright,” or “Thanks, I’ve got it” would both be much better ways to say what you’re trying to say.
Holy cow, my wife would have a laughing fit if she saw me giving advice on how to be polite. 
ETA: Actually, “No problem, I’ve got it” is better than “Thank you, I’ve got it.” Not sure why, but it is.
Actually, this whole thread points out something…yes, you CAN go wrong with an explanation, because quite frequently the explanation will not be accepted. If you answer “Sorry, no”, then there’s not much that the asker can say. If you say “Sorry, no, he’s a bit stressed out right now” or “Sorry, no, he’s not really socialized yet” then Mom and/or her child will insist that being petted will make Pups feel better now. “Sorry, no” will not allow for a counterargument as to WHY the kid should be allowed to pet the dog.
People, both adults and kids, have gotten into the habit of assuming that rules are made to be broken, and that if they can just argue long enough, they will get their way. By simply stating “Sorry, no” with no explanation, there’s nothing to argue with.
If you are that darn antisocial and crabby then AT THAT point you can politely tell them to fuck of. Its a win win for you types.
And if someone argues with you, you can write them off as an idiot and walk away. Especially when we are talking about a stranger who you will never see again.
There’s no rule that says you have to subject yourself to every fool you encounter out of politeness.