The problem wasn't the reboot, the problem was the reboot wasn't enough of a departure from the old movies. Also, they should have avoided the origin like the plague. Because not only was the origin ground ALREADY covered it took up screen time meaning elements from the first movie got pushed into the sequel.
No origin would have made the reboot seem fresh and chances are there wouldn't be apathy towards the sequel. Forget the reviews, a character like Spidey should be critic proof. My brother (a casual movie goer) confirmed this by saying he wasn't bothered in seeing ASM2 because ASM1 was average (his words not mine).
If ASM2 underperformers I think it will be more to do with the first movie than the second.
Honestly, I think you're both wrong.
The problem wasn't rebooting
or redoing the origin. It was playing too safe. They were testing the waters too much. They didn't even go in-depth with the origin enough, much like the Raimi film, leaving almost only the surface details on top, much like the Raimi film.
What the first film should have done is focus more on Peter's high school life. Develop characters like Flash and Sally Avril more. The first film got through the origin in the first 20-30 minutes and then quickly rushed him out of high school. The reboot should have been the anti to that.
There is no reason why the origin should automatically mean the film is plagued. Spidey arguably has the greatest origin of all time. Ultimate Spider-Man's first volume received critical acclaim. They should have done more things akin to Ultimate Spider-Man, particularly when it comes to the high school stuff. There were so many alternatives to the origin and ways to improve on Raimi's origin.
You could make the same argument for Batman Begins. Batman's origin is just as well known as Spidey's. Furthermore, Batman's origin would normally take
less screen time to establish than Spidey's. "His parents got shot, trained around the world, came back and he's Batman." But they made an entire origin film because they knew
how to explore the origin and go in-depth.
Plus, the origin is out of the way now. The reboot has gotten rid of that burden, so there's no reason why that should still play a key factor in this film's reception.