Fear of being a time bomb
The novel The Fault in Our Stars by John Green describes some of the difficulties cancer patients undergo when trying to maintain romantic relationships. At first, Hazel doesn't realize the reasons why she doesn't want to let the friendly Augustus get close to her. She is initially unsettled and considers if she really finds him attractive. But then Hazel soon realizes that she wants to avoid Augustus falling in love with her and thus being hurt more by her death (p. 107). This fear causes Hazel to keep her distance from Augustus. Hazel is afraid of hurting the people who love her. She doesn't know how long she will live, but she knows that she will die early or could die at any time because of her cancer.
This feeling is reinforced by comments on the wall of Augustus' ex-girlfriend Caroline Mathers. There, friends of hers have written that they too have been wounded in Caroline’s fight against cancer (Chapter 6, 43%). After reading this phrase, Hazel starts imagining herself as a bomb: "Wounded. Like Caroline Mathers had been a bomb and when she blew up everyone around her was left with embedded shrapnel." (Chapter 6, 57%).
Protecting Augustus from suffering
Hazel cannot see at this point that love is worth the pain. She knows, after all, that she is actually very attracted to Augustus, that she has feelings for him and merely wanted to keep her distance from him in order to protect him:
So of course I tensed up when he touched me. To be with him was to hurt him— inevitably. And that’s what I’d felt as he reached for me: I’d felt as though I were committing an act of violence against him, because I was. (Chapter 6, 71%)
In order to protect Augustus, Hazel wants him to run away from her so that he can be spared the suffering caused by her death. This is also addressed in a later conversation between Hazel and Isaac about Augustus. Isaac suspects in this conversation that the reason Hazel keeps Augustus at a distance is because she is afraid that Augustus will leave her because it will be too much for him, just as Monica left Isaac.
'Do you like him?' Isaac asked. 'Of course I like him. He’s great.' 'But you don’t want to hook up with him?' I shrugged. 'It’s complicated.' 'I know what you’re trying to do. You don’t want to give him something he can’t handle. You don’t want him to Monica you,' he said. 'Kinda,' I said. But it wasn’t that. The truth was, ...