There are 2 reasons why a school would tell you off for torrenting:

1. "Abuse of Resources". While downloading, your torrent is using an awful lot of bandwidth, competing with everybody else using the same school internet infrastructure. When you're seeding, you can place an even greater load on the infrastructure, because most internet hardware is optimized for downloading rather than uploading.

2. Because somebody complained. Corporations that own copyrighted media will often monitor online torrents and send cease-and-desist letters to all of the IP addresses that are downloading or seeding it, and to the the internet service providers of those IP addresses. While you are on campus, your school is your internet service provider. If they got a letter saying that someone was downloading illicit copyrighted material on their network, they are legally obliged to inform you and to take some measure to ensure that you don't do it again.

Schools themselves don't actually monitor all of their internet for copyrighted material. It would place to much of a burden on them. They can, and sometimes do, block individual ports or protocols. However, most of the "I got in trouble for torrenting at school" stories are from people who got caught by the rightsholder, and the school was informed.

If you want to test this, try torrenting something that is not copyrighted. [The Internet Archive](archive.org) has a lot of public-domain files available as torrents. Technically, these files from WikiLeaks may also be okay. Alternatively, some more detail about the letters you receive would probably indicate how exactly you ended up receiving it. Does the letter mention a specific copyrighted work, or a corporation that holds the sole rights to copy it? Does it list your I.P. address? Or does it only mention traffic, terms of use, and university regulations?

As /u/mastigia said, torrenting isn't illegal. It was invented to do one thing very well: to move around very large files to a lot of people via the internet. Regular downloading has the following disadvantages:

• All of the traffic is placed on a single server, which gets expensive to run if many people are downloading a large file from it.

• If that one server goes down, nobody else can download the file, even though many people have copies of it.

• If your network connection is interrupted, you have to download the whole file all over again.

• If part of the file is mangled while you download it, you won't find out until you open the file, and then you have to download the whole file again.

• You can only download the file over one network connection, which is only as fast as its slowest component.

Torrenting addresses all of these:

• Files are downloaded from "peers": other people who already have the file. If any one person deletes the file or disconnects from the network, you can still download from all of the other people who are "seeding" the file.

• There is no centralized infrastructure (apart from the internet service providers) that is needed to make this happen. Anybody may make torrents available for free, and anybody may download them for free, and the only cost is their computer's electricity and their personal internet connection. Nobody needs to own a domain name, or an SSL certificate, or a server.

• Torrents are subdivided into very small "chunks". If your internet is too spotty to download a 20 gigabyte file all at once, you are still probably able to download a 2 megabyte chunk. As long as you can download a complete chunk from a peer before you lose your connection, you will eventually download the complete torrent.

• Each chunk is checked for correctness after it is downloaded. If it is bad, the chunk -- and only that chunk -- is redownloaded.

• You can only download a chunk from one peer, but you can download many chunks at once. If there are many peers, you can download many parts of the torrent at once. The only limit is how fast your internet connection is.

Because torrents can run extremely quickly, many schools block them so as to relieve stress on their network infrastructure. Fortunately, most torrent clients allow you to throttle your download and upload speeds. If you keep your downloading to 1 megabyte per second and your uploading to 100 Kilobytes per second, you should get no complaints. This bandwidth is completely typical for normal web browsing, and should not interfere with other peoples' ability to use the same network as you.

Because torrenting is a useful protocol that has actual, legal use cases, most schools and internet service providers do not explicitly prohibit torrenting. Most of the ones that do block torrenting, only block it to keep the network from being overused. If you torrent non-copyrighted material at a reasonable speed, you should have no problems. If you do get into trouble, you can explain why you did it and why you shouldn't get in trouble for it.