Why? I can think of another quick rule of thumb: never trust anyone who doesn't give explanation of the statements one claims.

Looking at the four nodes below "regression" and those below "classification" in the OP, we see they are the same. The reason is that the same methods can often be used for both.

This is what the comment means when it says the division between regression and classification is often artificial (i.e., imposed by people who are concentrating on taxonomy).

It's just a comment.

Can you explain why you feel that way?

He's making a fair point, which is that certain types of classification methods basically involve "fitting" a hyperplane to a dataset in such a way that the hyperplane divides the data into different classes [1]. In trivial cases, we may be able to do this in two dimensions, in which case the "hyperplane" is just a line bisecting two different classes of data. It's easy to see how this can be conceptualized as a type of regression.

[1] http://en.wikipedia.org/wiki/Support_vector_machine

Classification is regression with a discrete finite range.

Regression is often used to mean regression with infinite range, but especially since so many classification techniques are just searching for a regular partition of an infinite range, the distinction isn't made much anymore. Whether the rare techniques that are specifically over a discrete finite range still count as regression depends on who you ask - usually yes.

This is one of the first observations someone learning the subject would make.

It's often practically true, though.

While every method I can think of differentiates itself at a lower level than regression/classification, and thus has interpretations in each, it's not always feasible or easy to make the "flip". Often times the approximation steps that make the algorithm tractable depend on the objective function.