Strafer, I have a couple of hundred hours, and I promise you that every landing is not a corker for me. Don't know how long it takes to get to that point, but from speaking to some far more experienced pilots than me, I'd guess the answer is never!
I agree with FD, though - it's very hard to conceive of a situation where you can't go around, even after the wheels have touched. I've done it myself, many times. The only thing I can think of would be if there were obstacles at the end of the field, but I can't believe that would be the case at a field that's used for training.
Have a chat with your instructor, and ask him why he thought a go around wouldn't have been appropriate. And don't worry about the odd bounced landing.
FFF
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