Generally, an immigration officer can deny your J-1 visa application for a variety of reasons. However, the most common issues resulting in J-1 denials are:
DOS doesn’t believe that you intend to return home
They don’t think you have enough money to pay for your program without working
If you’ve been denied a J-1 visa, it’s recommended that you contact an immigration lawyer as soon as possible. In many cases, an attorney can analyze your case and advise you on whether you should reapply, and for what type of visa.