Wireshark on University Network

Can it compromise other network users's privacy/security? The short answer is, yes, potentially. It's a matter of to what degree.

University networks are usually pretty modern, so the wired network is probably fully switched, in which case you should only see traffic to and from your own PC, plus broadcast traffic. Also, any really sensitive traffic (for example, a user logging into his online banking account) should be encrypted. However, to the extend that you CAN see other people's traffic and it's unencrypted, there is at least the potential to see things that are private.

If the wireless network is encrypted, then you will be able to see other people's traffic, but it will not be readable. If the wireless network allows open, unencrypted access, then you will be able to read other people's traffic; at least other people using the same access point.

Use of Wireshark on the University network will have no impact, because Wireshark is a passive tool that does not generate any traffic, with one exception: If you have network name resolution turned on, Wireshark will generate a DNS PTR query for each new IP address seen. If you turn network name resolution off, Wireshark should have no impact on the network.

Using Wireshark in a computer network class is an eminently reasonable and sensible thing to do, and is very common. Many instructors have student exercises that require the use of Wireshark. If you think it might run afoul of your University's Acceptable Use Policies, then you should discuss it with the network administration staff. You might want to modify the course syllabus for next semester to include Wireshark, which would certainly bolster your case for using it in class.