Should universities no-platform controversial speakers?

Universities should be able to no-platform speakers because a platform grants legitimacy

Question: Should universities no-platform controversial speakers?
Position1 of 2›: Yes, Universities should be able to no-platform speakers
Argument1 of 5›: Universities should be able to no-platform speakers because a platform grants legitimacy

The best way to combat extreme ideas is to not afford them the space to spread.

The argument

Allowing universities to no-platform speakers and prevent their ideas from securing a platform to communicate would prevent their ideas being legitimised and reduce their public support. One example of no-platforming being employed successfully was in the case of Milo Yiannopoulos. He was once one of the most prominent far-right voices in the United States. However, he lost access to major conservative platforms in 2017 and his movement lost all momentum. He was forced to declare bankruptcy and lost all influence. Without a platform, the idea falls on deaf ears and is reduced to the margins of society. Universities should be allowed to deny anybody a platform they so choose to and play their part in preventing dangerous and harmful ideas entering the mainstream psyche.

Context

The public adopts and supports ideas that it sees as legitimate. Granting dangerous and harmful ideas a platform demonstrates that they are legitimate and recognised positions and opinions

Premises

[P1]Providing a speaker with a prominent platform legitimises their ideas and helps them gain public support. [P2] Denying controversial speakers a platform, as shown by the collapse of Milo Yiannopoulos's influence after losing major platforms, marginalises their ideas and prevents them entering the mainstream. [C] Therefore, universities should be able to no-platform controversial speakers to stop harmful ideas from being legitimised.

Counter-arguments

Former Breitbart editor Yiannopoulos did not lose support for his ideas because he was no-platformed. He lost public support because he appeared to make comments endorsing paedophilia. In reality, this case demonstrates why it is so important that the public engages in debate over inflammatory ideas and rejects the ones considered most abhorrent to it, as it did in the case of Yiannopoulos. Only then can dangerous and harmful ideas be truly refuted and combatted. Without a public platform through which healthy debate can be engaged in, extreme ideas can go unchallenged in the corners of the web.

Rejecting the premises

P3: To stop dangerous views gaining traction, you must publicly refute them. Therefore, public debate is essential.