Web premieres to fight piracy?

Double the sales. If people like a movie enough, they'll buy the dvd/bluray after having already seen it in the cinema earlier. You could compare it a little to mobile phones and game devices that constantly get released under slighly new versions. Or 'deluxe' versions of dvd's being released some time after the regular ones are released.

Also, consider the fact that a century ago, cinemas were the only place where you could watch a movie. If digital copies would suddenly replace cinema premieres, all cinemas would go bankrupt nearly instantly.

Web streaming can be pirated. Netflix has some of the better encryption to prevent piracy but even their stuff gets pirated. You can go to any torrent site and look up Netflix exclusive shows and find them there.

There is one way to watch latest movies if you can afford it. PRIMA Cinema allows for a secure connection to watch new movies but it costs up to $35,000 to get the hardware and another $500 per movie.

It's simply the business model the industry has used for as long as 'home media' has existed.

Film studios make money on ticket sales. Theaters make money on food sales. There is a symbiotic relationship there that home-media premiers would interfere with.

So that's how it's usually been done. Make money in the theater, then make money later with home releases (traditionally cable rights, and video rentals--now digital).

Of course, times chance and there are studios that now release films online and in theaters simultaneously. Magnolia Pictures is one studio that does simultaneous releases. Steven Soderbergh is a director that has also released films via simultaneous channels.

While the other answers explain what you asked about, I'll pop in this bit of news, published only yesterday, that says that what you call a "web premiere" is being considered as a possibility:

Napster founder plans to screen movies at home on day they hit cinemas

A new service that would make major blockbusters available at home on the same day they hit cinemas has been proposed by the Napster founder, Sean Parker, despite reports of major misgivings in Hollywood.

There is a catch, of course, directly addressing Catja's comment:

Parker’s startup venture, known as the Screening Room, would offer movies for $50 (£35) in the US, with as much as $20 going to compensate theatrical distributors for their potential losses.

In a more detailed article, they say that the movies would be available for 48 hours, so not "bought" in "bought the DVD/BluRay" sense, in an effort to keep the industry's profit as untouched as possible. Would it be enough to satisfy their hunger, while also attractive enough for the consumers, remains to be seen.

The first article also explains the logic behind the current "theatrical window", which was well addressed in some of the answers and comments already posted here:

Hollywood has long shown tentative interest in the concept of maximising revenues from premium home video releases by breaking the longstanding “theatrical window”, but in practice distributors and studios are terrified at the prospect of putting themselves out of business. The current window, usually 90 days, protects cinemas by ensuring movies are not available via video-on-demand and DVD until interest in viewing them at multiplexes has been exhausted.

Not surprisingly, the studios are very unhappy with the idea. The first article also mentions Netflix' attempt to do this about 2 years ago, and how it ended (you can easily guess).