You are heading out of some institutional building that has the typical double glass doors that open where they meet in the middle.
Someone else is coming toward the building, about to enter. You do the polite thing of pushing open the door on your side, smiling at the person coming in, welcoming her to use the door you’ve opened.
She does exactly the same thing with the door on her side.
Each of you uses the doorway you’ve opened. No one accepts the offer of the open door.
We have had our hopes extinguished hundreds of times. Yet we persist.