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Which I why I hate that wording, because that means "divide b into a" is equivalent to "divide a into b parts". And that's just confusing.

It feels to me as though far too much of any given field uses redundant (the same concept expressed lots of different ways) or misleading (something made to sound far more complicated than it actually is) terminology and causes unnecessary amounts of confusion among anyone trying to learn it.

But it loses its English meaning for a=1. Whereas, "divide ten into two" would make sense.

I'm with you on the wording. The word "into" is ambiguous on its own and even more ambiguous used with "divide." There's a discussion of that here: http://mathforum.org/library/drmath/view/52296.html

As an example, a person can easily read "divide 24 into 6" as "divide 24 into 6 [parts]," i.e. 24/x = 6, x = 4 — as opposed to 6/24 = x, x = 0.25. This use is especially reinforced by everyday experiences like dividing a cake into eight slices.