Question: Why is it said that BitTorrent is faster, partly, because it transfers random pieces of a file instead of transferring it from start to finish in a contiguous/linear fashion?

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**EDIT:** But why do they *have* to be 'random'? Why not a more predictable 'semi-contiguous' transfer in which one peer gives you the first half, and the second peer the other half? This would theoretically reduce overhead.

Answer: 
Most responses don't seem to be answering your question.

**BitTorrent is not faster.**

It's actually *slower* because of the overhead of connecting to multiple sources.

The real difference in practice however, is you are downloading from many sources that can **potentially add up** to be faster than what a website could give you. Many web servers are under heavy loads or are otherwise speed-limited so you don't suck them dry.

The fact that BitTorrent transfers the file in a seemingly random order has no direct affect on its speed.

In regards to your edit, the **pieces are not random!** They are prioritized based on rarity: a rare piece needs to become less rare as fast as possible so it is not lost if the source that has it suddenly leaves. It has to do with availability, not speed.
Say you send two people to the grocery store to pick up a list of items. You give them each the exact same list. However, one of them must pick up the items in the exact order they appear on the list. The other may pick up the items in any order they please. Which do you think will finish first?