I can offer at least a few reasons why I feel this to be true:
1 - Since the recession, the shift has been toward the employer, with companies becoming more particular about whom they hire, and with job seekers being forced to settle for lower-paying jobs as their unemployment benefits run out. Companies have come to realize this and exploit it, leveraging this to hire only what they consider the best workers, for the lowest wages possible. The best defense against this is for the workers to be as flexible and versatile as possible, enabling them to option themselves to potential employers in several fields.
2 - Technology is changing rapidly and - along with it - so is the job market. Jobs that weren't in demand, or perhaps didn't even exist just a few years ago, are now showing very rapid growth and expansion. The worker who only learns one skill is at a distinct disadvantage when vying for these rapidly-changing markets.
3 - In an effort to be more profitable, companies have slashed legacy compensation packages, cutting such benefits as sick pay, vacation time, eliminating pensions, etc. The employee who stays with only one company, or only one job market, shuts themselves out of seeking the best options for their future.
4 - Companies have shown that they no longer feel any responsibility to provide even a gesture of loyalty to their employees, with layoffs and cutbacks the order of the day. With companies no longer feeling the need to show gratitude and loyalty to their workers, why should the workers feel any need to be loyal to their employer? It's become a dog-eat-dog world, every man for himself. Companies put their own well-being first above all. Employees should do the same.