I'm curious as to WHY we should apparently cut the hand of a thief as a punishment?

“[As for] the thief, the male and the female, amputate their hands in recompense for what they earned [i.e. committed] as a deterrent [punishment] from Allaah. And Allaah is Exalted in Might and Wise.” [Quran 5:38]

Please relate answers specifically to answer the question: 'WHY'

And for bonus points: hypothetically: if I am a shopkeep/homeowner/lawmaker should I cut the hand (or fingers or whatever) of (assuming they are proven guilty and are not poor/have any good reason):

1. A child that steals from my shop/home
2. A mother that steals from my shop/home
3. A man that steals from my shop/home

Related Questions:

1. Where do we get the idea of beheading, stoning and hand-mutilation in Islam?
2. From where the hand of the thief should be amputated?