This is, if you'll pardon the expression, horseshit! It implies a supernatural/metaphysical/undefinable/magical thread linking us one to another, without providing any evidence for such a thread. We must take it on faith, just because someone says so? I think not!
While we may all be a part of the whole, it does not necessarily follow that we are all an equal or integral part. The universe has a way of tossing parts aside haphazardly, to the benefit of some and the detriment of most. Which side of the equation you end up on is mostly a matter of luck."A human being is a part of a whole, called by us _universe_, a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty." ~ Albert Einstein
I am always compassionate when interacting with myself. And selfish, too. It's a lot less messy than interacting with anyone else.Yes it will be a glorious time when we interact with ourselves compassionately instead of selfishly.