Overpopulation of the Earth

By overpopulation I'm referring to humanity growing so large it ruins the planet and hence we become extinct.

This is EXTREMELY unlikely for 3 good reasons 

1.  Extensive studies have shown that when nations reach about $8000 GDP per capita the birth rate starts and continues to drop.  Since the 1800s the poverty rate worldwide has dropped from 80% to 10% and is continuing to drop, so birth rates will continue to drop worldwide, developed countries average around the rate required to maintain the same population.  Progress is by far the most powerful prophylactic.

2.  In the 1800s a farmer in the US (or in undeveloped countries today) produced enough to feed his family and one other person,  now the average farmer in the US produces enough to feed 200 people, so as third world countries continue to develop and their farmers become more efficient they will soon produce enough to feed themselves and more, running out of food is highly unlikely. 

3. The US is now a net exporter of fossil fuels, something noone could have predicted, so the odds are other resources will be found or technology created that will extend our ability to exist with the resources we have.