There are four distinct reasons someone wants to shut down a speaking event:
Any sort of social event of a certain political bent is, net net, a win for that political side.
I have discussed this in a separate answer about the purpose of gay pride parades, there are tangible political benefits - from like minded people having an event. Whether it is a show of strength (hey, i'm not one of only two people like me around, powers that be!), to increasing own morale (hey, there's a ton of us!), to just socializing/networking. A speaking event adds on an informational component - the speaker presumably informs/teaches the audience something.
By shutting down a speaking event, you deny those whose politics you dislike that set of benefits.
As a reverse, it's an effective political tactic.
When opponents shut down your events, you get demoralized. Especially when they do it with clear "yah, fine" from The Man (in this case, campus administration).
Some people just feel better about imposing their will on others.
This was explored in the infamous Stanford
prison experiment. You give someone power, and they enjoy exercising that power.
It creates a general chilling effect on one's political opponents.
If someone on one political side sees that their opponents can shut down a famous celebrity speaker using threats of violence, you can be sure they would shut up and not speak up on campus about their own political views, out of simple self preservation.
Additionally, specific to the topic at hand, the events are being shut down by radical progressives (mostly in USA).
Before delving to specific reasons why on their side, let's dispense with the expected propaganda claiming that "they are opposing nazis". This sort of "deplatforming" has very little to do with "nazis", "alt right", "Trump" or any other excuse. First, because 90%+ of those who are deplatformed aren't by any stretch of imaginatuion "nazis", even if they happen to hold right wing or conservative views (and, increasingly, left wing views in most topics). Second, by virtue of the fact that it started back in early 2000, when 'nazis' were meant as members of Germany's National Socialist German Workers' Party; "alt right" wasn't a thing and Trump was famous for casinos, not politics and was still a Democrat.
So why is it that it's the progressives that is intent of not letting people who they disagree with speak?
It is due to the progressive's ideological inheritance, mostly Gramsci (with a further ago influence from Hegel).
I'll try to expand on this later, but a very good analyzis is in the 2004
book "Gramsci's Politics of Language: Engaging the Bakhtin Circle and the Frankfurt School" by Peter Ives; and its somewhat dense academic writing can be summed up thusly: language is materialistic (in Marxist sense, not physics sense), and therefore, speech and language informs and influences social reality, and therefore he who controls speech, advances towards controlling that reality.
This is in direct opposition to Milton/Locke tradition of free speech.
An somewhat different explanation is offered by left wing professors in the following form: deplatforming is "simply choosing the information that the students get to hear (or not to hear), as is the job of academy". Why it is that they get to decide based on their own political views - and not any sort of academic criteria - is not coherently explained in that article.