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This is a general science-related question, so no necessary definitive knowledge needs be comprehended before hand.

I've been wondering what science lovers feel or think about the idea that science can't explain everything. Cause, there are definitely so much that Science have not reach yet. I believe because the subject of science can go everywhere and in a topic where, "proving," is vital, it is conflicted with the variations of life. Such as extraneous variables. How should a scientist handle that? why?

I believe that our science is flawed due to the fact that humans are the measure of everything. We created the abstract and the definitions. By our comprehensions, the theory may be right. But if we can't prove it, which for most theories we can't at the moment then it's not 100% true.
Man is prone to error.

Also science can only explain something that the human mind can comprehend. If we lack the ability to comprehend it, doesn't mean it doesn't exist. We just lack the ability to comprehend it, whether completely or at the moment( Look at the black whole theories for example of this. We didn't understand them because we couldn't comprehend them. Now we sort of do.)

However, Science is created and used by man. To not point out the flaws of mankind would be... rather incomplete. I'm not saying in the above statement that science is powerless. It gave us a lot of things such as the wheel all the way to nuclear power. But, you have to see my point to. A lot of our science is theoretical. Things such as gravity, evolution, black holes and other things we take for granted are technically theories. We don't know if they truly exist(black holes is what I'm hinting at here. We detect irregularities, but we have never *seen* a black hole. Only it's effects. Or the white hole, complete opposite to a black hole. Those ought to exist and we have mathematical proof of it but no other proof than that.)
So, not all science is based on on proof, but inference as you've correctly state above. If we infer and our inference in inherently wrong due to our inability to comprehend the other possibility, what then? If we cannot comprehend something, it doesn't mean it doesn't exist. And since it's not comprehensible, we can neither infer about it nor explain/prove it.

See what I'm trying to say? (Wrote this at 2A.M., so it may be hazy.)

Oh Vedun, white holes can't exist because they can't be created. Black holes, on the other hand, have both the physical ability to exist (just a lot of mass compressed into not a lot of volume) and the mathematical theory to be proven to exist. Now see, a black hole is simply a place in the universe where the escape velocity from the event horizon of the hole is equal to the speed of light. Since nothing of which we know can travel faster than the speed of light, anything inside the black hole's event horizon cannot escape.

The escape velocity is how fast something has to be going away from a center of gravity in order to escape its gravitational pull; escape velocity from the Earth is about 17 m/s, if I recall correctly (and I'm too lazy to look it up). The event horizon of a black hole is the radius (the Schwarzchild radius) from the "singularity" within which an object cannot escape. So the escape velocity from just outside a black hole is nearly the speed of light, 3.0 x 10^8 m/s, or 300 000 000 meters per second (very fast).

So a white hole is the opposite of a black hole. It would therefore be something nothing could get into unless it was travelling faster than the speed of light. Since nothing can exceed 300 000 000 m/s, nothing can get into a white hole--and since nothing can get in, it can't actually exist. On the other hand, anything can travel less than that, so anything can enter a black hole, so it can exist (and indeed, they do--at least, probably. Google Cygnus X-1).

Most scientific laws pretty much don't have exceptions. If there is an exception, the law itself becomes trash, replaced by whatever satisfies the exception. Like the Law of Universal Gravitation. Show me something that defies the law of gravity, I dare ya. Let's see, what other laws can I cite that don't have exceptions...? The Law of Conservation of Momentum, the Law of Ellipses (planets' orbits are elliptical), Newton's Third Law (for every action, an equal and opposite reaction), et cetera. I wonder if there's some kind of encyclopedia of laws...

Scientific laws are essentially general statements about the behaviour of things, so if an exception is found, then the law is either disregarded or modified.

It must also be said that laws will often have limited scope. Newton's laws of motion, for example, are valid approximation at low velocities only, and classical laws of physics do not extend to the very small scale.

I am actually very aware about the incompleteness of science because I studied it so long. The same is true of everything: study something long enough and you find that it has a foundation more insubstantial than air. In the case of science (physics specifically) I found that there are quantum states (Heisenberg Uncertainty Principle) that are not just unknown by humans, but actually unknowable by definition.

Newton's laws are only simplifications of Einstein's relativity laws. Except they came first. But relativity equations simplify to Newtonian ones at low velocities. So Newtononian physics are not limited, just incomplete, and have since been made more complete by Einsteinian...er...relative physics.