Border officials have a lot of power in the United States. They can and do turn many people away each and every day.
One reason they do it is if they think that you are lying to them. For instance, even if you have an immigration visa, something you say may cause the officials to think that you lied to get it. They can block you from entering. Don't give them a reason to think you're being dishonest or that you ever were in the past.