It's interesting that $14000/month is "rich" on this website, and some people earning $100/month actually own houses. Meanwhile people making $50000/month in San Francisco can't afford a house because half of it is taxed away and housing is astronomically expensive.
If your net pay is $7000 per month you absolutely can afford to own a house, you're just being fussy about the house you want.
I'm not familiar with the situation in San Francisco. But in Santa Cruz, the cost to own with a 20% down payment is ~50% higher than the rent for the same unit. If you can't afford a substantially higher down payment, you're not really in the market for a home.
With $7k/month after tax, you would probably be renting an 1br, or maybe a cheap 2br. But your income is not high enough to buy anything, unless you start looking for homes well outside the town.