I know that's what they say in their reminder emails, but it's very misleading. Basically, people can't write a review after they have seen the review of themselves. The mechanism is designed to prevent retaliatory reviews.
So you get a window of a few weeks in which you can write a review. If you leave a review, then you get to see the review about yourself straight away. But if you don't review, then you have to wait until your own window has closed. After that, you're able to see the review about yourself regardless of whether you left a review yourself – because you are no longer able to leave a retaliatory review.
Airbnb aren't very clear about this at all, and that certainly pushes people to leave reviews, but it's a side effect that Airbnb play up, not the actual designed purpose of the review system.
That's not true. You can see what the other party wrote without writing a review if you can wait for the review period to end, which is 14 days -- not that long. It must be so because reviews are public.
So you get a window of a few weeks in which you can write a review. If you leave a review, then you get to see the review about yourself straight away. But if you don't review, then you have to wait until your own window has closed. After that, you're able to see the review about yourself regardless of whether you left a review yourself – because you are no longer able to leave a retaliatory review.
Airbnb aren't very clear about this at all, and that certainly pushes people to leave reviews, but it's a side effect that Airbnb play up, not the actual designed purpose of the review system.