There are a lot of factors.
The lackluster economy is one of the biggest, if not the biggest reason. There are many workers, but not as many jobs. This classic supply-demand curve problem leads to a lower price point, manifesting in unemployment, under-employment (part-timers, college graduates working as baristas and Uber drivers), low-quality/dead-end jobs, and general wage decline. This is a general global issue, encompassing everything from European youth unemployment, the Chinese "Ant Army" generation, Arab Spring uprisings, etc.
There is housing cost pressure in core metropolitan areas clustered around major cities, but especially acute in those areas considered "world cities", like New York, San Francisco, Los Angeles/San Diego, Tokyo, Beijing, Shanghai, Sydney, Paris, New York.
Urbanization, overpopulation, and migration are the causes. More and more people being born, and moving to cities - whether it is two or three immigrant families sharing an apartment in an ethnic enclave, college roommates or recent graduates from outlying regions sharing rooms or couch surfing in a major city, young interns and professionals sharing rooms, laid-off factory workers from small company towns, or drought-stricken/indebted farmers abandoning their farms/kicked off their farms. Because housing demand is high and supply cannot increase fast enough, adults live with their parents or join in with others to outbid others for housing. My own* examples from just the past decade of renting has included a single mother with two children living in a one bedroom, a trio of immigrant families living in the two apartments on either side of me (6 families total), a mother with a late twenties adult son in his sixth year at community college living next to me, a retired couple with two adult sons in a two-bedroom unit adjacent to me, six young college students/waiters sharing a three-bedroom unit upstairs, etc.
People say this must be due to zoning laws or NIMBYism, but neither explain this worldwide phenomena of population growth, urbanization, migration, immigration. Tokyo has great mass transit and tiny closet apartments, and yet the greater metropolitan area is still the world's largest at some 36 million people.
I also think that as scarce resources (such as jobs and money) are increasingly drawn from the periphery into a retreat and concentration to the powerful core - along with increasing centralized, automation, efficiencies, and rising productivity - it isn't just the bright lights and big cities that shine as a beacon or magnet of opportunity, but also, big cities are now the places where most of the remaining opportunities exist.
After all... mechanization, automation, consolidation (get big or get out), and imports means the factory jobs (there were once some 50,000 more factories in the U.S. 40 years ago than today) and the agricultural jobs (that once employed half of all workers a little over a century ago) are gone. And yet in 1900, the U.S. had something like