VERY poor reasoning. It is not mere "free speech" which gives a person "entitlement to huge public platform". Instead, "free speech" guarantees the public right to speak, in private and in public locations. But it is the regular offering by officialdom to all comers to a given ("huge public platform") venue, that gives yet another a would-be speaker the right to also seek, and use, that venue to speak, without discrimination based on the content of their proposed speech.
The people who advocate shutting down Milo Y's speech are not merely advocating violating his First Amendment right to speak, but also are advocating the government violating his 14th Amendment right to equal protection of the laws: They want other people to continue be allowed to speak at the UC Berkeley campus, but not Milo Y.