Nonsense, of course you can prove stuff in science...
It depends on what you mean by "proving". I would categorize "proving" hypotheses true in science as probabilistic. At some threshold, say when something is 99.9999999999999% probably of being true, then we consider it "proven". That probability is damned close to being certain. But in a philosophical sense, it is not certain...merely highly probable.
The problem comes when people who do not grasp statistics latch onto the idea of uncertainty. They might latch onto that hypothesis that is 0.000000000001% of being true and "root for it as an underdog". They do not grasp that something with such a low probability of being true is false. It is virtually impossible for it to be true. Thus the growth of fringe theories that have been scientifically proven false, and yet continue to be believed. (My opinion on the cause of this is that certain religious sects promote unquestioning belief in authority, which promotes habits of mind to believe whatever their own authorities tell them).