Your analogy is not adequate!
As I mentioned in my comment above, what does it mean to "turn off a human"? It's hard to understand your analogy in the first two paragraphs because this notion is decidedly unclear. Turning off a computer means you are putting it in a state of rest; essentially of no activity. The closest equivalent for a human would be sleep, but if you wanted some hypothetical condition you could invoke some sort of "cryostasis" (cryonics/suspended animation). You should note, however, that computers are not currently ascribed any rights so you do not ask your computer if you want to turn it off, but you would certainly ask a human if s/he wanted to be put in cryostasis. But it's also not a bad thing to turn off a computer today because turning off a computer doesn't harm the computer (in fact in some ways it is beneficial). It is not the same way with humans. Although there are many cases in which I think cryostasis would be awesome (I'd totally do it if we had the technology today, just to wake up 500 years from now in the super high-tech future! ^_^), there are differences in that humans have bonds and connections to the real world which would be severed, causing great harm if done involuntarily. Your analogy, I'm afraid, is not adequate for what you are trying to convey.
Based on your updated definitions...
I mean smart, I mean, appears to be the same as a human, which doesn't mean its "sentient"
Unfortunately, the analogy becomes even less adequate, because a (merely) "smart" computer is not conscious. We don't prescribe moral protections to rocks and shrubs and spoons and fancy "SmarterBot" programs because they lack conscious awareness. And that's why it's appropriate to turn them off. It's not appropriate to "turn off" a human because we are conscious, not because we have something "special" inside us.
"Smart" vs. "Sentient"
Then consider if a computer becomes as smart as a human, you still
intuitively know that turning off the computer is not a bad thing to
do and turning off a human is a bad thing to do.
Originally you wrote "smart" and I had hoped you meant "sentient", but you've indicated you mean merely knowing lots of data but not sentient. Since we do not afford unconscious entities moral protections, as mentioned above it does not get you anywhere to compare turning off (destroying) a computer and turning off (killing) a human being.
You write after:
What if the robot (computer) can do everything a human can do? What
then? If you cannot tell the difference between the robot and the
human then how would you feel about turning off the robot?
Well, provided it still wasn't sentient, there would be no problem with turning it off. It is obviously quite theoretically possible that one could create a robot that mimics human-like behavior such that it is indistinguishable from a human but lacks actual sentience. It get's a little hazy, however, when you start getting that complex because sentience is not really a well-defined concept in philosophy or computer science. What is "awareness"? My robot could have video camera eyes and microphone ears, thus allowing it to perceive the environment, but does that mean it's aware of the environment? Need it be aware of itself in relation to the environment? Need it be aware that it is aware? Etc.
Size matters not
We all have axioms of reasoning, but I believe many other people have
this axiom as well.
I am sure many people believe this ...
This is not a good way to start an argument; it does not matter how many individuals believe in an idea, it doesn't mean it's any more true. Take any widely held myth, or any particular religion you want. If your logic was correct then Islam would be the most "true" of all religions, and I'm not sure you want to say that... :P
"So the question is, what is the soul/spirit"?
You are correct in assuming that there is a distinguishing characteristic between humans and man-made machines. We are not the same. But "souls" are not typically used to characterize this difference in modern philosophical debates and even less so in scientific ones. The problem with souls is that they're so hard to prove. It would be sweet to have a soul (honestly). I'd love to have one. But they're entirely unverifiable. Outside philosophy, souls are dismissed as pseudoscience because there is no evidence to support their existence. One needs not invoke the concept of a soul to explain any real problem facing us today. Within philosophy, they aren't really talked about much anymore because from the outset they lack any sort of philosophical justification. There are philosophers who currently are dualists (who would generally accept the notion of a soul), but their numbers are thinning...
The distinguishing characteristic you are looking for is simply
- flesh vs steel/plastic
- DNA vs. BIOS
- Brain vs HDD (or SSD if you're a hipster)
If you are looking for a distinguishing non-physical characteristic, I think you'll be hard-pressed to find one, although it will depend on which philosophers you talk to. Any physicalist (i.e. non-dualist) is going to dismiss souls and assert that logically (computationally), a human brain is just like a computer. Sure, it's wired a bit differently, and the wires are made up of different materials, but it's functionally the same.
Onto this idea of "specialness"
I feel this is an important question because it has consequences which
may be real consequences in the future if we do develop smart robots.
Yes, the future—our future—is going to be very, very interesting. ^_^ There will probably be sentient robots before we die. The only question is: are you going to shut off these poor computers like they are merely toasters, or are you going to afford them some respect so they don't go all iRobot on us? :P I say this jokingly, although there is a tinge of seriousness to it because I feel like the "axioms" you describe, this "specialness", are at the heart of the problems of the past (and now) with sexism and racism and fascism and all these "ism" problems; they always seem to come down to this same "We're special" idea. White people are special, let's enslave the black ones. Pure German people are special, let's kill everyone else. Men are special, let's not let women vote or to get paid as much. The institution of marriage between a man and a women is special, let's not let gay's be married. Maybe I'm just a weirdo, but I don't think us humans are all that special. It is quite natural to think as humans that we are special, that we are not mere "animals", but after really examining that notion I was at a loss to really justify it in any way. It dawned on me that really we are no more special than the lion in the savannah, whose fierce hunting skills and sharp claws are perfect for exactly what it does, or the salmon in the river or the eagle in the sky in much the same way. We are not intrinsically "above" them; in fact in many ways we are far below them. Henry Beston in The Outermost House wrote,
“In a world older and more complete than ours [animals] move
finished and complete, gifted with extensions of the senses we have
lost or never attained, living by voices we shall never hear. They are
not brethren, they are not underlings; they are other nations, caught
with ourselves in the net of life and time, fellow prisoners of the
splendour and travail of the earth.”
I guess what I'm getting at here is that I would encourage you to investigate the real reasons why you have this idea that humans are "special"; take a look at where those axioms came from. I could be wrong but I don't think you'd suggest that you were "born" with such an axiom. At some point it was acquired. If you can figure out where it came from and why, perhaps you can try to analyze whether it's based on a valid belief.
Sorry I rambled on a bit; this is a common question I get because I'm interested in Artificial Intelligence, and thus why I tend to have a lot to say. I hope I answered your question adequately. :)