I actually like that exchange a lot. What people around here don't seem to understand is that Raimi (Like Lucas, who couldn't pull it off) was shooting for an old-fashioned sense of melodramatic romance. He's paying homage to old Hollywood love stories. Hence, the dialogue reflects this actually quite nicely. However, because its unabashedly sentimental and slightly corny people graon and proclaim "THATS NOT COOOL! SPiDERMan IS SuPOSED To BE AWeSOME!.!".
Raimi succeeded in doing that really great. That's part of the reason that my parents and grandparents loved that movie so much and it made such a truckload of money. It spoke to multiple generations of film lovers in a way that Hollywood usually ignores by focusing solely at pleasing hip, cynical teens/20-somethings who can't appreciate writing that isn't drenched in "cool" irony or, the most dreaded of all, "realistic".