Your dad doesn't distrust you, nor is he punishing you. He just doesn't know what to do since your older sisters had babies while still young, and he probably feels responsible even though he shouldn't. You, on the other hand, see that you are being very respectful of his wishes even though you like your friend very much. I am really glad to see that you understand that sneaking behind your parents' backs would only make it worse for all of you
May I suggest a compromise? Choose a time when you and your dad are both in a good mood. Begin the discussion by telling him that you understand why he hesitates to let you date. Tell him that you would like to prove yourself and learn how to act on a date. Ask your dad if you could have a few of your friends (boys and girls -- no couples) including the boy you like over to your house for an afternoon or evening. Make it very informal -- watching a video; playing sports; working on a project for school, church, or your community. I am sure you can come up with a fun activity where your parents can not only see you in action, but can get to know the young man, too. In other words, try to get involved in activities that are not formal dates. That way you can learn about guys and yourself and how to interact and how to say no. At the same time, your parents will see how you are able to handle yourself and that will build their confidence in your ability to handle yourself on dates.
If your parents don't like this idea and still don't want you to date, then look at ways you can still be friends with this boy at school. This doesn't mean going behind your parent's backs -- it just means that you can still like him, talk with him, and get to know him better. One day, when it is okay for you to date and he asks you out, you will have an even better time.
I wish you the best and remember that you will always be ahead when you talk to your folks and look for ways to solve your problems as a family.