That explains why the movie had to be made. Doesn't explain why they had to do the origin... again. When I saw the trailer at the movies, there was a collective groan from the audience when they saw it was the origin again. Should've just started us off on a new Spider-Man adventure.
Yes, that's true, and I totally agree it should've been a new adventure.
For the origin reason, it's beause everyone tied to Spiderman 3 were asking for a lot more money to stay on board and the studio felt more damage would've been done to recast everyone in the same canon; over simply taking the easy way out and starting over again where they could keep control of the director, writer, and direction of this new "storyline".
This ties into the fact that past director Sami Raimi was heavily urging to have more control over the potential Spiderman 4 than he was allowed with the prior films, which (imo) did become a lot more disjointed with 2 and 3.
Since the last film came out 5 years ago as well, they didn't think the "fanbase" and backbone they've built up was worth latching on to. Although that certainly hasn't stopped other films.
So in other words, Sony's being Sony.