Perhaps the Court or the government could produce an test for self-represented people looking to appeal. The test would be unrelated to the litigant's case. The result would feed back to the litigant a test result which tells him his chance of failing on technical grounds.
In this matter, the result might tell the father: "Your understanding of how to argue an appeal is low. Even if you have a good case (and we don't know if you do), you will probably lose and there is a real danger of you having to pay the other sides' legal fees.
The system as it stands seem unnecessarily cruel.