I live in the UK and I regularly read the Guardian. I'm not sure what that has to do with twitter, save that they are both private organisations and can impose their own rules on their own space. Why do you care? If you have a blog, you can do this yourself. Or not. It's up to whoever owns the space isn't it?
I don't see the relevance of the UK police's behaviour. This story is about twitter and how they are trying to control their own space. They are allowed to do that, regardless of what you think. Why you think the UK police are connected to twitter is a mystery to me.
If Twitter decides that any threatening or harmful tweet is to be erased, half of Twitter could end up being thrown out. It's too bad their new CEO is on the warpath about this.
This is an obvious straw man.
People who received threatening tweets or whatever, could always just log off and stop seeing them.
This gets to the heart of the matter. Of course people who are threatened could just go away. But I think that the overwhelming majority of people want the people doing the threatening to go away. I guess Twitter, a commercial organisation, has made a calculation that they would prefer the people who threaten others to leave. It's their site and it's entirely up to them how they manage it, what sort of behaviour they want to allow and what they should do about people who won't behave.