To 'go spare' originally meant 'to be extra' or 'to be unemployed/unused'...as in "I have three tickets going spare for tonight's performance". Only in the late 1950s did it take on its more usual modern meaning of 'to become very angry'. In that sense, it is much the same as 'go OTT' or 'go over the top'. The same idea exists of there being something too much or superfluous about the rage involved...ie there's more than enough of it, given the circumstances. So, in a way, it still means 'extra'.