I suspect that the books were trying to teach you western knitting and you unvented eastern knitting.
The names were given, originally, because western was popular in western Europe and eastern was popular in eastern Europe -- or something of the sort. I prefer to say that when you sit facing north, the fronts of your western stitches face west, and the fronts of your eastern stitches face east.
That is, western stitches face west if you knit off the left needle onto the right needle, which is the more-common method. If you knit off the right needle onto the left needle, you have to sit facing south to make it work.
I think we ought to call these two directions "northern" and "southern" to correspond to "eastern" and "western", but we have no names for them at all -- though off the right onto the left is called by many clumsy, inapt names: "wrong way knitting", "mirror knitting", "left-handed knitting", and "knitting back backwards" are all I can recall off hand.
Quite a lot of people have learned to knit in both directions so that they can knit flat without having to turn the work over. I never learned to purl southern style, but I can manage to knit off the right needle onto the left well enough to manage bobbles and the pointed garter-stitch edging from Medrith Glover's peacock. Which I have to re-design[1] into purling on the front rows to get around my inability to purl on the back rows.
As has been previously mentioned, Mary Thomas's two-volume set (_M.T.'s Knitting Book_ and _M.T.'s Book of Knitting Patterns_) is the work to take to a desert island if you've only room for one knitting reference in your trunk.
Anything by Elizabeth Zimmermann is good, and her _Knitting Without Tears_ is required reading.
Once you think you can knit a whole sweater, you need to read Barbara Walker's _Knitting from the Top_, to see how easy it is to design sweaters that fit perfectly. She has also written three stitch treasuries -- all four books are have been reprinted by Schoolhouse Press. (And, of course, Schoolhouse keeps all of E.Z.'s works in print.)
Vurra strange: even if you throw in all my embroidery books and a box of iced-tea spoons, my sewing books take up less of my needlework shelf than my knitting books do -- and *not one* of the sewing books is a must-read, while nearly all of my knitting books are books I could recommend with enthusiasm.
Is it just that Mommy taught me how to sew long before I started collecting books, or is sewing so complex that no one book can be definitive?
Joy Beeson