The best time to begin your own business is when you don't need the money. Most people don't look for a second income until they are faced with a financial crisis, which means their options are limited. Since they need money right away, they are forced to take a job that pays a salary, as opposed to starting a business that they enjoy but that may not generate income right away.
Another reason people are reluctant to start their own businesses is the often quoted statistic that 90% of businesses fail. The problem is that there doesn't seem to be any research backing up this number. In fact, research from the Small Business Administration indicates that two-thirds of new employer establishments survive at least two years, and 44% survive at least four years.
Furthermore, the way the statement is worded is quite misleading. Saying that businesses "fail" gives the impression that they couldn't make money to survive, but the reasons that business close vary widely. Statistics show it is often due to poor management or financing problems. However, businesses can also close due to lack of interest, the size of the workload, or simply that the owner found a better opportunity.
If you are doing something you enjoy, your chances of success are much higher.
If you are going to make one move this year to try and improve your personal finances beyond the well-established basics (creating a budget, paying down credit card debt, contributing to retirement accounts, etc), it should be to begin your own business.