Contrary to popular belief, it's actually derived from a old (very old) German word(s). Here is a good explanation:
The name "Boxer" is supposedly derived from this breed's tendency to begin a fight by standing on its hind legs and "boxing" with its front paws. According to Andrew H. Brace on his "Pet owner's guide to the Boxer" this theory is the least plausible explanation. He claims "it's unlikely that a nation so permeated with nationalism would give to one of its most famous breeds a name so obviously anglicised".
German linguistic sciences and historical evidence date from the 18th century the earliest written source for the word Boxer, found in a text in the "Deutsches Fremdwörterbuch" (The German Dictionary of Foreign Languages), which cites an author named Musäus of 1782 writing "daß er aus Furcht vor dem großen Baxer Salmonet ... sich auf einige Tage in ein geräumiges Packfaß ... absentiret hatte". At that time the spelling "baxer" equalled "boxer". Both the verb ("boxen") and the noun ("Boxer") were common German language as early as the late 18th century. The term "Boxl", also written "Buxn" or "Buchsen", in the Bavarian dialect means "short (leather) trousers" or "underwear". The very similarly sounding term "Boxerl" is also Bavarian dialect and an endearing term for "Boxer". More in line with historical facts, Brace states that there exist many other theories to explain the origin of the breed name, from which he favors the one claiming the smaller Bullenbeisser (Brabanter) were also known as "Boxl" and that Boxer is just a corruption of that word.
In the same vein runs a theory based on the fact that there were a group of dogs known as "Bierboxer" in Munich by the time of the breed's development. These dogs were the result from mixes of Bullenbeisser and other similar breeds. Bier (beer) probably refers to the Biergarten, the typical Munich beergarden, an open-air restaurant where people used to take their dogs along. The nickname "Deutscher Boxer" was derived from bierboxer and Boxer could also be a corruption of the former or a contraction of the latter.
"Boxer" is also the name of a dog owned by John Peerybingle, the main character on the best selling 1845 book The Cricket on the Hearth by Charles Dickens, which is evidence that boxer was commonly used as a dog name by the early 19th century, before the establishment of the breed by the end of that same century.
The name of the breed can also be simply due to the names of the very first known specimens of the breed (Lechner's Boxer for instance).
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