There used to be such a thing as a polymath, i.e. someone who had mastered all subjects (or at least a very large range of subjects) and could be said to "know it all". A walking encyclopedia, if you will. Granted, such people were the exception to the rule (for most of human history, people with anything beyond the most rudimentary education have been the exception rather than the norm). But during the Renaissance, such an achievement was considered attainable enough that it was held up as an ideal... the "Renaissance Man", someone who was talented and accomplished in many different fields of human endeavor, not just an expert in one area. One thinks of Leonardo da Vinci as perhaps the most famous instance of a Renaissance Man. There is also the more recent example of Goethe, who is described on the back of one Penguin Classics volume as "scientist, critic, autobiographer, letter-writer, sage, statesman, conversationalist"--and all this in addition to his biggest claim to fame as Germany's greatest poet.
Many people have noted that it has become more or less impossible to attain the status of polymath in today's world, given the explosion of information and the ever-increasing fragmentation and specialization of knowledge that this has created. Today's academics tend to focus narrowly on one subcategory of a subcategory of a subject area. Indeed, given the sheer quantity of what there is to learn in our 21st century world, it is enough of a challenge just to become an expert in one subject, let alone all (or even just many) subjects.
But there is another factor that further complicates the picture and adds to the difficulty of knowledge mastery, and that is the ever-accelerating rate of change in today's culture. In the past, once you mastered a subject, you didn't need to learn a whole lot more to remain a master in that field. Today, in many areas, there is no end to the learning required to stay on top of the latest developments in the field. This is especially true of technology, of course, but applies to varying degrees in other areas as well.
One problem this creates is that depth of learning becomes far less important than learning just enough to keep up and continue to function without falling piteously far behind the curve. After all, what good is it now if you became an expert in a 1995 version of a certain software package or programming language that has changed dramatically since then, but which you failed to keep up with? Many types of knowledge have an increasingly short shelf-life and become obsolete almost as quickly as they become "necessary" to maintaining one's professional expertise and skill set. Why should we invest the time and energy in learning the latest thing in depth when the knowledge will be useless a year from now? Why not learn just enough to get by? It's sort of like cramming for a test just to pass the test, without caring if we retain the knowledge for the future or truly learn something deeply. After all, how can we explore the ocean depths when we have to spend all of our time just treading water? Better yet, why should we care to learn something deeply when the knowledge will be worthless a year from now?
The end result of this ephemerality of knowledge is that expertise and depth in a given subject area is becoming less and less possible with each day that goes by. But perhaps more to the point, it is not so much impossible as it is increasingly irrelevant. Much knowledge in today's world is only "knowledge" for a brief time, then is discarded like yesterday's newspaper, as relevant and useful as last week's weather forecast, as sought-after as the last decade's fashions. Under these conditions, why invest more time and effort into learning something than you really have to?