Are they being clingy or are we not releasing?

When I was younger, I asked my teacher where is birth and when is death. He answered, " everywhere all the time."
It took me a while to really comprehend this idea, which I naively took it as babies are born and people are dying everyday.
We like creation, birth and greetings. But when it comes to dissolution, death and goodbyes... We refuse to let it go.
Be it bodily, relationships or intellectuals... The idea of accepting an end is as if cutting a flesh out from our arms. Then, we suffer.
Come to think about it, is it we who refuse to set them ( an idea or emotion) free or is that we thought that they are clinging onto us?

Are we mistakenly holding on to death and in turn blocking the progression of birth?
Just like holding to a rope, so tightly. That if we are so fearful to let it go, we'll get rope-burn, till we learn how to free ourselves.