My back hurts when I do sit ups..?

That could be a permanent problem but...

I had that problem. I solved it when I bought a futon and I folded it into 3. I use that to do my situps on and put my feet under a desk. My back problems turned out to be caused by the hard floor and now I do 70 sit ups 3 times a day without any back pain.

I also stop immediately if I feel any sharp pain in case I've pulled a muscle but I push through discomfort or pain that slowly grows as my reps increase.

Not to be rude but there is a good chance you are doing it wrong.

Look at military sit ups, these are the best type of sit ups.

Try doing them slowly and one at a time every 10-15 seconds for 2 minutes it will help and not hurt as much

Then don't do them. It will injure your back more. Always, warm up, and stretch before doing any strenuous exercise. But if you're doing sit ups and not warming up, you can do more harm to your back. If you are doing stretches and warm ups before doing sit ups, then don't do them and see an orthopedic doctor to see why it hurts.

If you have back pain then you have to required to take physical daily exercise and Acupuncher.

Don't exercise and your back pain will go away.

you probably are doing them wrong

Because you don't believe in god :).