after 10 years of renting you will have nothing
A really simple calculation with the numbers from http://homeguides.sfgate.com/calculate-30-year-mortgage-bala... I will be nice and assume that the monthly cost of renting is equal to the monthly mortgage payment. Usually renting is cheaper. I'm ignoring the mortgage interest deduction, but also property taxes, homeowners insurance, maintenance, etc.
After 5 years of renting you have: 5 times 12 times -600 = -36000. After 5 years of owning you have: 5 time 12 times -600 + your equity. your equity is $100,000 - ~$93,000 + difference between what you bought it for and what you sold it for. And that last term can easily be negative. It only takes a 7% decline in value to wipe out the first 5 years of principal payments. If your property declines in value 10% and you sell after 5 years you come out behind.
The numbers for 10 and 15 years respectively are 16% and 29%. Now consider that the average home value in places like Stockton fell over 50% during the great recession.
If I would have had the money and foresight to buy the brownstone in Brooklyn that I was renting, I wouldn't have even had to bother with the working and saving for 10 years part, but you don't need to rub that in on a Saturday morning.
Given the area and amenities I want from a property, I save significantly more money renting and can live somewhere I actually like; unless I decide to commit to the country for 10+ years -- and I would lose my entire cushion of savings for startup runway funding in the process -- renting makes a ton of sense, even though at the base level the equation of "paying money for someone else's mortgage vs paying money for my own" seems a no-brainer.