How to select vertically in textedit using keyboard

Solution 1:

The problem with that is that the Mac's modifier keys Command and Option are used in conjunction with the arrow keys to navigate through text more quickly by going to the beginning or end of a line or the beginning or end of the next/previous word, respectively.

There may be a utility that will allow you to modify the system-wide defaults but you run the risk of breaking text editing everywhere in the system.