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.