Why train Olympic Lifts?

Because they're awesome.
Seriously though, it's a good question and there's a good answer (I think). Here goes.

There are a few point to share that go into my thinking about training.

1. People should be striving to improve themselves; Be “Better Than Yesterday”.
2. Improvement can (and should) be objectively measured; see “What is Fitness“.
3. Most people aren't as strong as the could be; see “How Strong are You?“.
4. Therefore progressive strength training is important; enabling greater work capacity, generally.
5. Fundamental bodyweight exercises and powerlifting movements are relatively simple to learn* and develop strength well.
6. Almost all physical activities require the application of strength at speed –> Power.
7. One of the best ways to develop power is Olympic Lifting.

*Before all you powerlifters get upset, I'm not saying powerlifting is simple, just that it is less complex than Oly lifting. 🙂

So if you want to improve your performance at pretty much any physical endeavour, train the Olympic Lifts.

Have a look at this video for a bunch of different athletes from Catalyst Athletics performing Power Cleans.
Note the sort of weight they are moving. Think about their potential power output. Why train Olympic lifts? Now you tell me! :O