Why throw away so much sourdough starter? Tartine Book no. 3 this is the first time I've use this site to ask a question:

I've been meaning to bake some sourdough bread for a long while. I've been just hung up on the recipe for the starter.
A book I'm currently using for inspiration says to do roughly a 1:1 ratio of water to flour of 300 g warm water and 315 g flour. Eventually, just before feeding the starter, it calls to "Transfer 75 grams of the starter to a clean bowl and discard the remainder of the starter." Later it then asks you to continue this process, discarding the sourdough and leaving 75 grams. 

When I first read this I had to blink. Discard 540 grams of sourdough starter?!? What a waste!

Why is this book telling me to do the in the recipe? This seems incredibly wasteful. I don't understand why I couldn't just keep feeding it with a 1:1 ratio.

The book is TARTINE, Book No. 3 By Chad Robertson.
At the beginning, you are throwing out a lot because you are just feeding the culture. You're just seeding the growth medium (fresh flour and water) with the young culture, so you want to be sure that the ratio of food to culture is appropriate.

Once the culture is established, you don't have to throw out any, but you do have to keep feeding it. This generally means that either you throw out a little, or have to feed it a ton. At the bakery where I work, we use so much starter that we don't throw any out. We're left with little enough at the end of the day that we just add fresh flour and water.

The ratio of starter to fresh flour and water (and ratio of flour to water) are used to control the culture. Different strains grow better at different levels of hydration, and leaving more of the already cultured starter in when you feed it can leave in more of the "waste products", like acids, which contribute to flavor.