Because I would gladly write for you guys.
Please don't take this in a snarky way, but realize that a lot of people would gladly write for them.
The last threads I saw on the subject were basically this; Paizo has a lot of talented writers working with them already and they do not actively solicit new authors. The one area I may be mistaken on that is with PF Scenarios. You may be able to submit an idea through there. Check out those threads for more information.
Otherwise, start writing for a 3rd party publisher, and get noticed. Build a resume of good writing, and make yourself known in the industry and to the Paizo staff. In general they look to experienced authors who are already in the industry.
Obviously, I'm not Paizo staff, but you may not get a response right away due to GenCon. I hope that helps, and good luck.
To a certain degree, having to ask the question counts as a tick against the successful applicant.
RPG Superstar is the shortest answer. Every year Paizo has a contest that is open to anyone. The rules are clear and there are are set goals with plenty of advance warning. Submissions are judged and then voted on. People are advanced through tiers of submissions and the final winner gets a paid commission to write a module.
As Gray says, Paizo has a stable of established authors they can trust. People who turn in their submissions on time, every time. People who follow the guidelines established for their commission and require little to no trimming or padding, and little to no heavy editing. People who they can rely on.
The public? The public keeps screwing up. Time and time again. Hundreds of submissions for first-wave RPG Superstar that just can't follow the rules. Formatting failures, word-count issues, egregious mechanical mistakes, you name it. There are dozens of posts where the judges themselves explain what qualifies for auto-disqualification in their eyes. And yet.
So Paizo doesn't take blind submissions. They've got a method for back-door entry to their list of authors.