Perhaps a better question is "Why is anything normally distributed?" It appears originally to have been a simplification to make the math more convenient:
As Rand Wilcox reports, "Why did Gauss assume that a plot of many observations would be symmetric around some point? Again, the answer does not stem from any empirical argument, but rather a convenient assumption that was in vogue at the time. This assumption can be traced back to the first half of the 18th century and is due to Thomas Simpson. Circa 1755, Thomas Bayes argued that there is no particular reason for assuming symmetry, Simpson recognized and acknowledged the merit of Bayes's argument, but it was unclear how to make any mathematical progress if asymmetry is allowed." (Wilcox, p. 4)
Wilcox, R. (2010). Fundamentals of modern statistical methods: Substantially improving power and accuracy (2nd ed.). New York, New York: Springer.[1]
As Rand Wilcox reports, "Why did Gauss assume that a plot of many observations would be symmetric around some point? Again, the answer does not stem from any empirical argument, but rather a convenient assumption that was in vogue at the time. This assumption can be traced back to the first half of the 18th century and is due to Thomas Simpson. Circa 1755, Thomas Bayes argued that there is no particular reason for assuming symmetry, Simpson recognized and acknowledged the merit of Bayes's argument, but it was unclear how to make any mathematical progress if asymmetry is allowed." (Wilcox, p. 4)
Wilcox, R. (2010). Fundamentals of modern statistical methods: Substantially improving power and accuracy (2nd ed.). New York, New York: Springer.[1]
[1] http://amzn.to/2tkMRoI