Because a 'safe space' is just a name, much like 'pro-life' is a name. The titles that people assign to things do not always properly illustrate what's actually going on.
The idea of a safe space is to actively remove and prevent discussion that is contrary to the emotional well-being of other users. This is a problem because it's curating ideas from a website just because they are in opposition to someone elses' worldview. If some user's twitter account is promoting anti-feminist beliefs, then a feminist can chime in and claim that the user is creating an 'unsafe space' for them, thus getting the user's posts removed and their account suspended. The original problem was that the feminist chose to read the anti-feminists posts, but that doesn't matter in a website that's trying to curate content rather than to allow people to communicate with others as they choose to.
The only context I've ever heard "safe space" in was for a space in which protected groups had the freedom to speak without fear of harassment or being spoken over. As in, insular spaces like a club meeting in a university, or the back room of a coffee shop, or a specific space on the internet. As in, defined "this is a safe space for X" places. I personally think there is certainly a place for that in the world, but I don't think anyone worth listening to is advocating for twitter as a whole to adopt this philosophy.
As for making twitter
safer, it's impossible to have a perfect moderation team that only bans things "worth banning" because what is "worth banning" is unclear. Going too far in either direction (lax curation or extensive curation) both produce stuffty side effects. Clearly some kind of balance has to be struck.
I believe the argument actually being made, at least by people like Anita, is that twitter is imbalanced towards "too little moderation". That's why this committee has been assembled. As someone pointed out, there's a range of beliefs among those they picked for this committee, so I think that a good balance will be struck.
There is an option to report people for having a different opinion.
https://support.twitter.com/forms/abusiveuser
If you had looked a bit further, you may have noticed that they don't screen content unless it is explicitly against their rules.
Firmly believing that something is good and true and right (Or at least better than what we have now), and wanting something to be changed are mutually inclusive.
If you look at basically any popular youtuber you'll see they have lots and lots of hate comments. Most are buried underneath the top comments, but they're nonetheless there. Same goes for twitter, it's just a lot harder because the UI is crappier.
~REMOVED LINKDUMP~
This is only scratching the surface of the youtubers and celebrities that decided to do entire videos dedicated to hate comments. There are likely thousands more that haven't decided to do any. I could spend another hour and get another 50+ links for you if you want, but I think I've made my point. You cannot possibly tell me that popularity does not attract hate without some sort of evidence.
And yes, it is basically the same circumstances that led him to get the hate specifically of the religious extremism type, yes. The point was double, to show that trolls and idiots are not somehow specifically targeting her and her alone, but simply because she's popular and has political opinions (which everyone does), and that there is absolutely no harm being done. He takes it in stride. It fuels him. It's not a good thing that he's being attacked, no. But it's certainly not causing any harm, so where's your evidence that it's caused harm to Anita? Sure, she's expressed sincere disappointment before but I've seen no legitimate emotional (or otherwise) harm.
I'd like to stress that. Harassment is not good. I'm not saying people should continue to harass, but you're blowing it out of proportion yourself. She's not a baby, she can handle 13 year old trolls saying mean things to her.
You're trying to tell me that I'm not allowed to cite the expertise of people who have devoted their entire lives to studying sociology and feminism? Let's compare:
Me: Support of multiple doctorates in Sociology (30+ years of relevant experience and studies and thesis')
You: Conjecture.
You can want for something to be changed without wanting it to be legislated. For example, she could want private websites like reddit or tumblr or twitter to curate their content towards her worldviews. That is not in violation of any sort of legislation, it would just be a company upholding some rules on a platform that they own. And websites already do this.
Linking a bunch of videos of people getting hate comments isn't really conducive to an argument. We can't compare the magnitudes of harassment that different people with videos or articles that they put together because obviously they're posting some arbitrarily sized sample of the whole. How much hate mail a person gets relative to other people isn't all that we should take into consideration when considering the seriousness of it anyway. She clearly gets a significant amount of harassment. Whether or not someone like Richard Dawkins would take it in stride is irrelevant to how it effects her emotionally. And of course you haven't seen this harm. Anita has a professional persona she keeps throughout her public appearances and youtube videos. There isn't really an opportunity for you to see the emotional effect any of this has had on her. And once again, you're downplaying her harassment to "13 year old trolls".
You're claiming to understand the extent to which she is harassed without being her or having seen her inbox or having read the tweets she gets. You can't just say I'm "blowing it out of proportion". You're just downplaying this harassment because it suits your worldview, not because you actually have an understanding of the extent to which she is harassed.
You can cite their expertise, but you can't use their viewpoints and beliefs as some sort of benchmark for the collective consciousness of feminism and sociology. Especially since you're just saying that they agree with you and I can't actually verify that.