One has to sift thru enormous amounts of information in order to find out what is true and what's not regardless of the information source. Doing so online is much faster than doing it in a hardcopy library.

Though, libraries may still exist, when the infrastructure to uphold the internet is long gone.
Anyway, that is not the point I wanted to make. What I wanted to say is that the teachers and lecturers in schools and universities have done the sifting already and so present to you what they have found to be important. And no matter how wrong they might be, on what is important, the fundamentals they have to teach you. That way you can get a faster overview of many scientific fields than by carving out the basics of them all by yourself, and I see it as highly important to have a basic understanding of many fields, to get a grip of the big picture.

It is a problem that many people are dwelling solely in their special field of expertise and that they cannot see beyond their own nose. That's why economists see every aspect from an economic point of view. It's what they know, what they have learned.
But to understand what's going on on this planet, to get the full picture and to make wise decisions for the future, you have to have knowledge of many different realms.
We have divided science in many areas, but in real life this division often doesn't exist and so a problem can touch aspects of many scientific fields. So if you watch a problem from your specialized point of view it is likely that you are missing something crucial, which could have dire consequences.

So, school is a way, to get in touch with those many fields, in a fairly compact span of time. For more in-depth knowledge you might fare better to do your own research, but for some basics, school is good enough. At least, where I live.

What I'd like to see in school though is the teaching of critical thinking from first grade on. That way pupils would learn to scrutinize what they were taught and it would get more difficult to distort the truth. So far the establishing of a critical mind is not only neglected, it is even discouraged. And that is, maybe, the point, where the school system really fails. It creates zombies that are willingly believing everything that a so-called authority, be it a scientific, political or clerical, spews around.

...the teachers and lecturers in schools and universities have done the sifting already and so present to you what they have found to be important.

You're right, of course, but what educators have found to be important has been sifted thru the filters of their own bias, and that of their instructors in turn. I suppose this is just human nature and is to be expected. The internet exposes learners to every sort of bias and thereby forces them to construct their own filters, if they're capable of doing so.

It is a problem that many people are dwelling solely in their special field of expertise and that they cannot see beyond their own nose.

I know this guy who does research on growing hybrid poplars for celluosic biofuel conversion in a semiarid region where the soil pH is 8.2 and the mean annual precip is 8.2". He utilizes computer controlled solenoid valve irrigation and knows precisely what micronutrient supplementation the trees require. I would imagine that he's the world's foremost expert on growing poplars under conditions they aren't adapted to. Yet there is no market for his trees, which I call his "bananas in Alaska." Has he ever asked himself WHY he thinks he needs to grow these trees that nobody wants where they don't belong? The reason he does it is that there's grant $$$ available for cellulosic biofuels research. To him, this is more than sufficient justification for this waste of the taxpayers' $$$.

So far the establishing of a critical mind is not only neglected, it is even discouraged. And that is, maybe, the point, where the school system really fails.

In the first place, few students possess the intellect to support critical thinking. For the few capable of developing critical thinking skills, the schools are designed to ensure that they never do. If large numbers of citizens ever developed critical thinking skills, the status quo would collapse. Everything from politics & religion to organized sports would be seen for the scams they are. The powers that be can't allow that. And for the very few who are capable of developing critical thinking skills in spite of the organized childhood long attempt to prevent them from doing so... well, here we are. :)