Can somebody explain why country of birth is even important. I know it's in the constitution, but for a country that prides itself on the idea that anyone can achieve anything with hard work it seems a little hypocritical.
The US Constitution says that among other qualifications the President must be a "natural born citizen". Being in the Constitution - the highest law of the land - is what makes it important. "Natural born citizen" means the individual is a citizen based on the facts / conditions of their birth. Anyone born in the US is a natural born citizen. Current interpretation also includes individuals with at least parent being a citizen at the time regardless of place of birth.
You didn't actually answer the question as to importance. You just repeated what was already stated to be known, without realizing that all your yammering about being in the Constitution only demonstrates a lack of substance because of it. They didn't even ask what natural-born citizen meant. They asked for an explanation for its importance, and stated why they found it hypocritical. You didn't address the concern at all. Explain it.
It being in the Constitution means we must follow it until the Constitution is amended. Read the Wikipedia article if you want a full list of why it was included (mostly to avoid having a President with possibly conflicting loyalties) and the various attempts to change it (including Orrin Hatch trying to make the Governator elligible).