Some people who should not buy a house: for example, anyone who is planning to move in a few years. People with overextended credit are also probably not good candidates for homeownership. However, home ownership—instead of renting–appears to be a good idea for many people—particularly at a time of rising rents.
The graph from a presentation by NAR Chief Economist Dr. Lawrence Yun shows that families with homeownership have a much higher net worth than is the case for renters. Growth in mortgage equity and longer term price appreciation are the major assets for the middle class. The homeowner with a 30 year mortgage payment has a paid-off home after 30 years; the renter has a nice stack of 360 rental receipts.
And, of course, there are many lifestyle/social benefits that homeownership creates for families—better educational achievement by children, better neighborhoods, increased community involvement, among others.
These are good answers to the question of “Why not rent?”