Q:

Why is the whammy bar sometimes called a "Tremolo" arm?

Who coined or mis-used the term Tremolo for the pitch-bending mechanism often found on electric guitars? 
Tremolo cannot actually be effected by using the 'whammy bar'.

A:

Fender corporation is a major contributor to the confusion of the term tremolo and vibrato, at least within the world of guitars.  They marketed the Stratocaster as having a "tremolo" arm, even though its use produces vibrato.  In addition, they had amp models, notably the Vibrolux, which were labelled as having a vibrato effect, even though the circuit produced tremolo.
The company itself recognizes this misapplication of the terms, c.f. Fender's discussion on tremolo/vibrato,

A:

The correct technical term for this kind of tailpiece or bridge arrangement is vibrato bridge or vibrato bar. "Vibrato" is a rapid, regular modulation of a note by varying its pitch up and down; this is what such a tailpiece or bridge can be used to do.
This kind of tailpiece or bridge is most commonly refered to as a tremolo bridge, although this is a misnomer. One definition of "Tremolo" is a rapid, regular modulation in volume, not pitch. (the more common definition of "tremolo" is a rapid back and forth alteration between two or more distinct pitches, like what you can do on a piano or organ, or again, a rapid trilling of one pitch, like what you can do with a pick or your fingers on a mandolin or guitar.)
Both "vibrato" and "tremolo" are classical music terms (in Italian) which have been in use for centuries and applied to playing techniques for all kinds of musical instruments and the human voice, long before the vibrato tailpiece for an electric guitar was introduced in the late 1940s by Paul Bigsby.
The term "whammy" is an onomatopoetic slang term that has come into use since the 1950s. It is most often associated with bridges that can perform extreme pitch bends, first the Fender Stratocaster design, and later the Floyd Rose and Kahler designs. I suppose the classical equivalent to the term "whammy" would be portamento, which is to say a slow slide from one pitch to another, not a rapid vibrating effect.

A:

I think the term Wham Bar or Whammy Bar came into use after Lonnie Mack's hit single, "Wham" which made extensive use of the tremolo arm.

