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: 
It's an availability issue. If you have to download contiguously, then you're dependent on people hosting more of the file than you. Every person with less of the file than you, will be unable to send you any data. 

If chunks are randomly distributed, the number of hosts you can download from will be higher, therefore you'll download the file faster.
Torrents aren't always faster, but when they are, one reason is network entropy. A connection of any duration (the download of a large file) may degrade over time, as random, uncontrollable factors affect the transmission of packets, such as router overloading and other problems between you and the server. More errors mean more retransmissions of packets, and this situation tends to worsen over time. Torrents make many smaller connections, across many routing pathways, a strategy that can, under the right circumstances reduce errors and lost or damaged packets, and seems to be faster, especially as the number of seeds and peers increase.