What does Buddha mean when he says, "In separateness lies the world's great misery. In compassion lies the world's true strength" mean?

I imagine
that you can interpret this in different ways, but to me, it is saying that what we human beings
need most is to feel that we are one with other people -- that we care for others and they care
for us.

In this quote, I think "the world" really refers to
people.  We are miserable because we are separate from others and we can often feel that no one
cares about us. At the same time, though, we are capable of making others feel very good through
compassion.  And what is compassion really?  To me, it is understanding how other people are
feeling.

So what I get from this is that, when we feel compassion, we are
actually becoming more at one with others and we are no longer separate and alone.