tbrooke, I'm sorry you're having problems. First, if he doesn't know about home health, it is understandable that he might worry. Second, how old are you? You say that you live at home. If you're under 21, and he's your dad, he probably wants to protect you. (My dad still wants to protect me and I'm 45!) Third, is this your first job? Fourth, being alone in someone's home might be less safe than a retail store or coffee shop when others are around. But even working late at a Starbucks with just one other person could be risky - that person could be creepy or even rape you.
So, as you go out into the working world, you need to develop "armor" to make sure that you keep yourself safe until you know that you can trust your coworkers and clients. And you should listen to your "instinct" - if you think someone is untrustworthy, don't dismiss those feelings. If possible, keep a cell phone with you.
My suggestions: Talk to your employer and find out what their clients are like, their ages and disabilities/needs. If you've never been a CNA before, the employer should work with you to start with by carefully selecting your first few clients. If you are having a training class, that would be a good time to ask these questions.
After you do all this, talk to your dad, tell him you know he wants to keep you safe and tell him the steps you've taken to keep yourself safe. If you took a CNA class, perhaps you could ask one of the teachers to talk to your dad? Asking your new employer to talk to him might be annoying to the employer, so I wouldn't do that unless you have no other choice.
Good luck to you.