This is a myth has been around since the 18th century, but the world is a really big place with plenty of space.
Let's look at how much land it really takes to hold 6 billion
people. To give you an idea, consider the small nation of Japan,
which has about 143,000 square miles of land. One square mile has
27.9 million square feet. Japan has a total of about 4 trillion
square feet, enough to give each person on earth 670 square feet. If
we housed people in families of four in simple two-level buildings
(8 people per building, one family of four per level), each building
could be on a lot of over 5300 square feet.
Using the American average of 8,000 square feet to house four
people, the entire population of the planet would fit into a space
the size of Texas and Nevada combined or less than the state of
Alaska. That leaves a bunch of unused space for growing crops,
sailing, and going on vacations.