For clarity, I'm going to try and restate your basic position so that we can address it in more detail. If I understand the question correctly, the idea is something like:
- If X and Y are similar on some grounds Z, then they should be treated similarly
- Our treatment of X is such that we do openly show it on TV and media
- Our treatment of Y is such that we do not openly show it on TV and media
- Therefore, X and Y are not similar in Z
And you're taking X and Y to refer to 'death' and 'birth' respectively.
First, I think there is some vagueness here with regards to what makes life and death similar and what the grounds for this similarity are. They are important asymmetries between them:
- Birth is a beginning (and generally seen as good), death is an end (and generally seen as bad). There is definitely an asymmetry of good and bad things. On a philosophical level, the broad analysis of the doing/allowing distinction and how it applies to harm and benefit might be a place to start for that. With regards to the media, negative news is often seen as more relevant and informative, and in line with media responsibilities.
- To compound that, death is usually the death of an actual person with a history and a life. A birth is the birth of a 'potential person', which is not nearly as significant because there is no narrative to tell about them. 'Potential people' hold few relationships, have made little impact, and are generally not rich existents in the same way actual people are.
- Death has first-person value to us. We have a relationship to death that we do not have to birth because we cannot apprehend or anticipate it. Our birth is the beginning of but not a part of our lives.
Second, I'm not sure if the 'X' you are mentioning is death at all. It seems to specifically be referring to commonly reported-on or depicted death, such as crime or war. These are not just 'deaths' but specifically types of death that are generally seen as unnatural. I'm not sure what the motivation is for saying that the 'taking of life' is a fundamental aspect of our existence. A large part of the current state orders, at least in the West, seem predicated on the idea that 'taking of life' is something undesirable. People shouldn't be taking lives. War is bad and we want to avoid it, crime is bad and we want to eliminate it, lives are only taken when there are unnatural circumstances.
The general idea that the modern state should ultimately seek to prevent citizens 'taking lives' and engaging in violence seems a pretty fundamental aspect of most non-anarchial end-goals. Hobbes and Rosseau propose fundamental models of statehood that are different in many ways but seem to agree that the desired end-goal is limited wielding of force achieved through the process of creating a state. Even a Marxist vision for utopia would eventually reach a stage where the violence ends.
So, crime reports and war footage are more acceptable in the news because they are more relevant and more newsworthy, they are actionable, they show fault-lines in society and problems for the government to fix.