My 2 reasons -
Libraries are designed specifically to be distraction free environments where one can focus. The internet might have all the info ever produced, but it is also the most distracting place ever created. And as more and more people get overloaded with info they aren't trained to deal with the craving for more focus and less distracting spaces is going to increase.
On the internet any half baked article passes for information. In the library the neuroscience floor doesn't have shelves and shelves of books written by kooks, that you have to wade through and filter out to find quality. This is huge advantage if you are doing any sort of serious work.