Take your pick from this buffet of possible options:
1) Sam Raimi had lost it by the time the third movie came out, and screwed the series up so badly that it would have been difficult to figure out where to take it.
2) Tobey was arguably too old for the part way back in 2002 already. He can't convincingly play an early 20s Spiderman. Same for Dunst. Plus, "classic" Spiderman is more of a teenager anyway. And heck, it seems likely that neither one of them would want to reprise those roles after so long either. I think it was a struggle to get them into Spiderman 3 as it was, IIRC.
3) Raimi wasn't interested in doing another one, and nobody was interested in following his vision instead of striking out on their own. Heck, there might have been legal requirements to leave Raimi's stuff alone and not build on it directly for all we know.
4) Reboots seem to work, while "fourth installment" is a less compelling draw for audiences.
5) Great opportunity to write a slightly edgier Spider-man including some of the anti-corporate paranoia that made the Ultimate Spiderman comic books interesting.