Why does "go spare" mean "get angry"?

Solution 1:

http://www.scribd.com/doc/31873955/Dictionary-of-Contemporary-Slang

spare 2 adj British
out of control, furious. The word, usually in the form ‘go spare’, has been in use since before World War II. It derives from the notion of excess

http://www.phrases.org.uk/bulletin_board/9/messages/572.html

SEND (SOMEONE) SPARE - (U.S. equivalent: drive someone nuts) See also 'go spare.'" From "British English from A to Zed" by Norman Schur (FirstHarperPerennial edition, 1991).

Solution 2:

According to Word Detective, go spare originally meant be made redundant, and the anger was a secondary effect:-

The original sense of “go spare,” when it first appeared in British slang in the 1940s, was “to be or become unemployed,” making it a close cousin of the more formal British euphemism for being laid off, “to be made redundant.” By the late 1950s, the normal emotional reaction to losing one’s job had colored the term “go spare,” and it had had acquired the added meaning of “to become distraught or very angry” (“When he saw what I had done he went spare,” 1958).

I can't say that I find this explanation particularly convincing, but I offer it for what it's worth.