If you are concerned who sees your tweets, you should be considering a private profile. If you want to avoid interacting with someone or seeing anything of theirs, you can block them. This seems very functional to me, and in line with the definition of "public" online communication.
But perhaps that difficulty was enough, and this was important to people who used the feature. Logically, blocking people from reading your tweets seems almost silly, because you can't really control who sees your tweets from a public account, but the illusion of control probably did a lot for the peace of mind of people who were being harassed.
From another perspective, Twitter is an institution that makes rules to govern the conduct of its users. Those rules are made public, and users can construct their own order on top of those rules. This is pretty much the principle behind rule of law - we get to know what's allowed and what isn't, and we can then construct our own arrangements on top of this foundation. Some people came up with some creative ways of using Twitter's rules to control access to their tweets, which is exactly the kind of behaviour one should expect. Then Twitter changed the rules, invalidating the order that these users had constructed. They're upset, and that's not unreasonable.
Sure, there's a principled argument to say that "public stuff should always be public". Twitter's new policy makes tweets much more like blog posts - you can decide which blogs and comments you want to read, but you can't decide who reads your blog. I have no real problem with that as a policy. But it's still the case that Twitter, seemingly without warning, changed a policy in a way that broke social conventions that their existing userbase had developed. That's legitimately annoying for those people.
Why do people put passwords on their computers? Anybody who has physical access can just remove the hard drive.
Why do people lock their cars? Anybody who wants to steal something can just smash the window.
There's no other comparable situation in which you'd make a public announcement and somehow expect some group of people who could hear it to not hear it. And let's be clear - every 'tweet' is a public announcement to the world at large.
Would you make an announcement on the 6:00 news and expect only some of the audience to see it?
Would you write a letter to the editor of your local newspaper and think you could exercise control over who reads it?
To invert it a bit, would you flag an email as spam and expect you could not mail the sender ever again?
The problem is, it used to work one way and now Twitter is (or, was) changing it with some really flimsy justification (now they can't tell when you blocked them! except there are other ways that worked). It'd be one thing if blocking worked this way from day one, it's another entirely to suddenly change it.