Airports are private property of the airport company, and they typically have separate restrictions for taxis. For example, LAX charges $4 per taxi [1]. Since rideshare companies are often operating under the legal fiction that they are not taxis, they don't want to sign a deal with the airports that treats them as taxis. But the airports don't want them not paying fees. So in this limbo they are not allowed to pick up airport passengers. But they can, and often do drop off passengers at the airport since airports don't usually restrict passenger dropoffs.

Airports make a lot of money off of use-fees like this. This is why, for example, rental cars are often much more expensive if picked up at the airport (SeaTac is a particularly painful example), as the rental car companies pay a hefty premium to be on site. At some airports, like JFK, there are some rental car companies that pick you up by shuttle and take you off-site (but it's a total pain and I recommend you do not do this due to the sheer hassle).

[1] http://www.dailybreeze.com/business/20131013/ride-sharing-co...