Lyric discussion by Zignor44 

Cover art for Take, Take, Take lyrics by White Stripes, The

The obvious meaning is that Jack White is very annoyed with fans bothering him. He shows the way an innocent meeting can become extremely uncomfortable for him, whereas the fans remain oblivious to both his feelings and also just how much they are escalating things.

But then there's the other POV of interpreting this completely free of any knowledge of Jack White. The lyrics have an interesting use of storytelling signifiers and characterization which, though subtle and sly, is an apt metaphor for the relation of fans to the famous. Through repetition of the phrase "that was all that I needed", the narrator's voracious appetite for experience with the famous is never satiated. He can't even tell a recognizable story about the interaction with a traditional beginning, middle, and end. It's all beginnings and false endings with no real climax. The real ending only arrives with his disappointment. Following a long trail of increasingly intimate interactions with Mz. Hayworth, he is shocked when she finally leaves in the most respectful way possible. It's possible that the only way such a story possibly could have ended was with disappointment, since the narrator continued to ask more and more from a stranger without any sign of being satisfied.

Meanwhile, Hayworth actually gets a story. She shows up at a bar, is bothered by a fan (though she never shows any direct signs of being bothered), and leaves when she presumably can't take any more intrusion (though we don't really know this for sure). She hardly has any voice even. Her communication is lipstick on a paper, possibly a written note to accompany it, and words of parting about being tired and saying goodnight.

Though the narrator communicates frustration and claims of being disrespected, his behavior throughout almost the whole song is transgression. Meanwhile, there is no evidence of any rude behavior from Rita, despite the narrator's claims. So there's an element of irony to the lyrics: the narrator is unreliable, and the reader/listener needs to think of themselves and look at the evidence before supporting one side or the other.

So what does all that mean? You can do whatever you want with it, but maybe it's fair to say that stories with a clear beginning, middle, and end, conflict that comes from both sides, and characters that have fully-fledged voices will read as more trustworthy to audiences.

Song Meaning
Negative
Subjective
Frustration
Celebrity
Fan Interaction
Storytelling
Irony
Disappointment