Why, according to Hume, do we have to be skeptical when regarding the inference of general principles from evidence?

It seems evident to us that when we see a certain certain cause and effect occuring together that we can assume a causal connexion between them. We have seen multiple times that when a billard ball hits another it transfers the impulse to the other ball. We establish a general rule through 'Induction' from observed instances to a general rule (e.g. in this case: a moving billard ball that hits another will always make the second ball move or if we have further evidence we might even conclude that moving objects that hit a still object move the latter). Hume says that what we assume when we draw this inference is that future instances will resemble past instances, namley the instances that we have observed (the uniformity principle). However, while we have seen the uniformity principle to work in everything we do, it is not proven to us. Tomorrow, the uniformities I have observed may not hold, while we all think we know that this is not the case, there is no way of actually 'knowing' it, we only believe this to be the case, it is not 'deductively' valid which means that there is no possible logical way for something to be not true. 2+2 will always be 4 as 4. It is inconceivable that it is not as it is not logically possible and it is independent of what does and does not exist in the universe , however, it may be the case that tomorrow the second Billard ball won't move after it has been hit because i can conceive of that happening and it would not be illogical and the universe could bring about a state where it does not happen.
The uniformity principle (The future will resemble the past) is not logically valid, I can conceive of it not being true and it depends on what exists in the universe. Saying that the uniformity principle has always been correct and therefore always will be makes sense but it is not PROVEN, it would only be proven if there were no conceivable way of it not being true. This is 'begging the question' or circular reasoning as I am using the uniformity principle to prove the uniformity principle. Saying that 'so far the future has always resembled the past and therefore always will be' draws on the supposition that 'the future always resembles the past' but thats exactly what I am trying to prove. I cannot prove something from that very premise because the premise would have to be true to prove the conclusion which it obviously is not because the premise I am using is exactly what I am trying to prove.