Sure, there's no life without death, but you're kind of underselling the Anthropocene Mass Extinction a wee bit, aren't you?
To be human is to have emotions, being sentimental is one type of emotion you can feel. Especially if you feel like Earth is currently being overrun and destroyed by humanity at breakneck speeds. To feel emotional about this OK, as long as you also stay grounded and realistic.
But we should not hide our emotions, it's possible to be both emotional and rational.
Just like arriving onto a crime scene and yelling at the crying survivors to shut up, without any consideration for the crime committed before, or any of its consequences.