For example. Robin Hood and Little John wish to cross the river using a fallen tree. Both begin crossing and confront each other on the log. In the story, Robin Hood refuses to retract and allow Little John to cross, Little John the same. We have a confrontation which created a conflict. However, if either party would have let the other pass, the confrontation would not have yielded a conflict.
... and Robin Hood and Little John would have gone their separate ways, and Little John wouldn't have joined Robin Hood's band and become his BFF.
Without the honest encounter, no meeting of the spirit and heart.
Aikido teaches the way of the honest encounter. Neither giving up and running away, nor making the other an enemy (which is my interpretation of saying Aikido is not about "combat").
But the honest encounter is also not about winning. It's about Robin Hood sitting up in the muddy brook and acknowledging that he's been beaten. It's about changing the terms of the encounter, because Aikido's not about fighting.
There's a fun video of Saotome Sensei out there giving a demo. Uke comes in with an attack and Saotome puts out a hand to shake. Uke looks confused and foolish for a moment and then shakes hands. Just a demo, but speaks to a core truth--Aikido offers a third way out. Change uke's mind, change the encounter.
But Aikido practice teaches finding the third way through martial competence. Without that, uke just beats you to the ground and it's over. Robin Hood has to be competent with the singlestick to stand on the log in the first place. Just ducking or avoiding isn't good enough--it's just a faster way to land in the brook.
And that's the paradox of Aikido.