This is the whole basis of Science. It is required to be provable, or it is just someone's opinion, and my opinion might be different to yours.
Perhaps you should research the Spanish Inquisition and the many atrocities committed by various religions for further insight into why this matters.
EDIT: Strictly speaking Science must be falsifiable
If you've got a conclusion which is invariant under all possible evidence, it stops being science.
It also isn't that difficult to demonstrate the underlying principles that are in action. The greenhouse gas effect is fairly easy to measure experimentally (it was first experimentally measured in 1859).
Modelling the climate accurately is a very hard problem but we don't have an untouched completely controllable alternate climate on which to perform experiments. It's still better than throwing up our hands and declaring understanding impossible.
It's certainly difficult to do; that is not the same as saying they are producing no valid & valuable information.
Public policy decisions cannot be based on "proof". There is never going to be proof positive of what the climate will do in the next 100 years until we arrive at 2113, and even then there will be aspects of the picture that will be unclear; not everything is easily measurable, and not everything you might like to know will be measured.
Actual science covers more ground than schoolwork where you have one variable and everything else is controlled. Climate change is a global-scale issues with innumerable variables that can not be controlled.
That's not the same as saying we can know nothing about it, or that we must make no decisions about what we can figure out with some reasonable level of certainty.
> Who decided exactly what inputs are needed for calculations and which should be left out? Who decided their relative weightings? Who decided the exact nature of the interactions inside the models?
Are you saying that because you don't know how to do this stuff, no one can make predictions with a reasonable margin of error?