First of all, classical mechanics is not only Newtonian mechanics. Rather, all physics done before 1900 is referred to as classical.
Secondly, as for "why are we learning wrong concepts?", I shall quote Richard Feynman:
"You might ask why we cannot teach physics by just giving the basic laws on
page one and then showing how they work in all possible circumstances, as we do
in Euclidean geometry, where we state the axioms and then make all sorts of deductions.
(So, not satisfied to learn physics in four years, you want to learn it in
four minutes?) We cannot do it in this way for two reasons. First, we do not yet
know all the basic laws: there is an expanding frontier of ignorance. Second, the
correct statement of the laws of physics involves some very unfamiliar ideas
which require advanced mathematics for their description. Therefore, one needs
a considerable amount of preparatory training even to learn what the words
mean. No, it is not possible to do it that way. We can only do it piece by piece.
Each piece, or part, of the whole of nature is always merely an approximation
to the complete truth, or the complete truth so far as we know it. In fact, everything
we know is only some kind of approximation, because we know that we do
not know all the laws as yet. Therefore, things must be learned only to be unlearned
again or, more likely, to be corrected.
The principle of science, the definition, almost, is the following: The test of
all knowledge is experiment. Experiment is the sole judge of scientific "truth."
But what is the source of knowledge? Where do the laws that are to be tested
come from? Experiment, itself, helps to produce these laws, in the sense that it
gives us hints. But also needed is imagination to create from these hints the great
generalizations—to guess at the wonderful, simple, but very strange patterns beneath
them all, and then to experiment to check again whether we have made the
right guess. This imagining process is so difficult that there is a division of labor
in physics: there are theoretical physicists who imagine, deduce, and guess at new
laws, but do not experiment; and then there are experimental physicists who experiment,
imagine, deduce, and guess.
We said that the laws of nature are approximate: that we first find the "wrong"
ones, and then we find the "right" ones. Now, how can an experiment be "wrong" ?
First, in a trivial way: if something is wrong with the apparatus that you did not
notice. But these things are easily fixed, and checked back and forth. So without
snatching at such minor things, how can the results of an experiment be wrong?
Only by being inaccurate. For example, the mass of an object never seems to change;
a spinning top has the same weight as a still one. So a "law" was invented:
mass is constant, independent of speed. That "law" is now found to be
incorrect. Mass is found to increase with velocity, but appreciable increases require
velocities near that of light. A true law is: if an object moves with a speed of
less than one hundred miles a second the mass is constant to within one part in
a million. In some such approximate form this is a correct law. So in practice
one might think that the new law makes no significant difference. Well, yes and
no. For ordinary speeds we can certainly forget it and use the simple constantmass
law as a good approximation. But for high speeds we are wrong, and the
higher the speed, the more wrong we are.
Finally, and most interesting, philosophically we are completely wrong with
the approximate law. Our entire picture of the world has to be altered even though
the mass changes only by a little bit. This is a very peculiar thing about the
philosophy, or the ideas, behind the laws. Even a very small effect sometimes
requires profound changes in our ideas.
Now, what should we teach first? Should we teach the correct but unfamiliar
law with its strange and difficult conceptual ideas, for example the theory of
relativity, four-dimensional space-time, and so on? Or should we first teach the
simple "constant-mass" law, which is only approximate, but does not involve such
difficult ideas? The first is more exciting, more wonderful, and more fun, but the
second is easier to get at first, and is a first step to a real understanding of the
second idea. This point arises again and again in teaching physics. At different
times we shall have to resolve it in different ways, but at each stage it is worth
learning what is now known, how accurate it is, how it fits into everything else,
and how it may be changed when we learn more."
And finally to quote Einstein, " As the circle of light grows, so does the circumference of darkness around it."