Some stories of human suffering draw more attention because there are some ways of suffering that are deemed more acceptable than others. Though it is generally agreed that suffering is an undesirable thing, it is a fact of human life, and the news media makes decisions about how to portray this fact in a way that will not disrupt their viewership, readership, or other audience. From culture to culture, opinions on what is appropriate in suffering differs. In some cultures, it is not at all appropriate to grieve openly; in others, it is encouraged. In the same way, the media chooses to present stories of suffering which appeal to a cultural conception of appropriate (and profitable) suffering.
When I say appropriate, I do not mean it is acceptable in the sense that there is a goodness to the suffering. Rather, the story being covered fits neatly or may even offer a stark contrast to cultural conceptions of what it is to suffer. People may prefer to engage with news stories about kinds of suffering they can relate to. Grief is a universal human experience, so stories of death thrive in news media. That being said, grief is dependent upon knowing a person or feeling that you know something about them. When Princess Diana died, the whole world seemed to mourn her. She was a very public figure with many details of her life publicized, so people had a ready concept of who she was before her death. In contrast, the deaths of "everyday people" do not draw much media attention because most of the audience will not have a concept of the person to grieve.
When it comes to more particular experiences of suffering, such as sexual assault or kidnapping, these stories may draw less attention because they deal with experiences that people would rather not think about. The media presents suffering in a way that makes people want to engage with that particular story, and subjects like sexual violence or crimes of racism may make people too uncomfortable.
The media also makes the decision to exclude stories of suffering which might make significant portions of their audience feel culpable. For example, crimes against people of a particular race or ethnicity are often ignored by the media in cultures where oppression of that particular group is systemic. Suffering occurs in the context of the global economy, like the exploitation of garment workers, is routinely ignored by media because the majority of people who engage with news media regularly consume or benefit from this suffering. Drawing attention to these kinds of suffering forces audiences to confront the ways they enable or benefit from the suffering of others, and people often don't want to engage with media which makes them, personally, feel bad.
When these particular stories of suffering are made public, it is often framed in the context of a tragedy, which implies the destruction of or fall from goodness. Such stories often provoke the question, "Why do bad things happen to good people?" These kinds of stories of suffering fit more cleanly into a cultural conception of good versus evil than the complex social reality which drives suffering.
There has developed a sort of feedback loop between media presentations of suffering and how this suffering is reacted to among the public. People sometimes engage in performative, recreational grief, outrage, disgust, or sorrow. Motivations for such behavior may include wanting to feel like a part of the group, tangential relation and validation of one's own suffering (past traumas or grief), or as a perceived form of activism. With this kind of response, media outlets must carefully choose and shape the stories of suffering they present so they can be sure people will not only watch, but also publicly (including online) speak about the experience.