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?