I agree with everything said. Look at it this way:
Initially you had every expectation you would pass and graduate, so you acted on that information. Sure this set people up for a false expectation, but everything you knew up to that point said it was a reasonable expectation. So far so good.
Next you find out that you didn't pass and won't graduate on time. (I'll get to more on this in a second.) You're in shock. In the middle of all this you talk to your dad. You haven't had time to come to grips with it, so you make something up. Not great, but it is human. He may not like it, but I bet he'll understand it in time.
Next you meet with your counselor and you salvage the situation! You can't beat that. I tacked an extra year on to my undergraduate degree by the time I was done. You're ahead of me!
Next you talk to your dad and you're sticking with your original story. Not great, but again this is human. This catches us up to the present.
This is where I'd pull the plug on the story you told your dad and confess everything. But don't fail to mention that you were still reeling from shock when you first talked, and that you'd only just found out you could still graduate at the end of the summer when you talked the second time. I would hope he could forgive you for that.
On the concept of failing: As an undergraduate I got a D in one class in my major, and two Fs in non-major classes. It killed my GPA, but I learned a lot. The D taught me that my study habits were terrible. I improved and got an A the second time through. The first F told me that I hate rote learning when it comes to history. Indirectly I found out I love history when it's not taught by rote. The second F was because I was skipping class to hang out in a machine shop. Since graduation I haven't needed the information that class was supposed to teach me, but two of my jobs since then required machining skills. Maybe this was my subconscious telling me something?
I don't necessarily see a bad grade as a failure. But it's a great opportunity to learn something that wasn't in the course curriculum. You mentioned that it was the subject matter that got you in the end on this course. Sounds like me and that history class!
Mend things between you and your parents, get ready for that class this summer, and set the guilt aside.