This is the million dollar question in Aikido.
You see, if we are able to forget everything and move like how nature intends for us to be, then we would have solve our dilemma, sort of. That would also means that we are becoming more like an organism, no faculty of self awareness, choice, autonomy and critical thinking, all the hallmarks of being ‘human’.

It Takes Time
Nature will take it’s time to work around things; trees will grow around an impediment, you will not see it today tomorrow, but over time, the tree ‘wins’. Sometimes we see a dramatic volcano explosion, or an terrifying earthquake, that happened suddenly; more often than not, it is a cumulation of years, decades or even centuries of work, grinding, moving, building up the pressure and at an instant, BOOM!
Just like nature, we need to understand things take time, and we can choose a path of willing, exercise our free will to train harder, train longer, put in more focus, study Aikido texts or we can simply choose to focus on something else.

Time or Timing
On the mat, it is usually about timing, you need to watch earnestly the opening, and also where your partner might be strong and where there is a pause in his movement and that is where you can apply countermeasures. Not everything can be countered, or forced. and if the point of opposition becomes predictable, mechanical, or cyclical, then the Aikido technique is dead.
That means if you as an Uke can catch your Nage at a stoppage every single time, then something is wrong, it might not necessarily be a Nage’s ‘fault’ nor it boils down to a uncooperative Uke, neither is the problem and also both possess the solution. The Nage needs to change something to break that stalemate, and the Uke needs to yield a little so that the Nage can continue with the movement.
This is the kind of subtle communication between Aikidokas in movement that takes years of practice to build, and this is what we train for, there is little spoken between movements and we read each other instantly, keeping everything in a stable flux. This is level of training, both Aikidokas melt into each other and then you can see no distinction between winning and losing. So much so it looks like a dance, except it’s deadlier.

No Competition
Naturally, when you don’t compete for pecking order, there is a more collaborative output, since we are not looking for winners by knockout, or winning by points.
In a competitive environment, there is no yielding, you can expect opposition at every given moment, and even if there is yielding, you can’t help but think if it is a feint. Once we put ourselves in a zero-sum game, everyone loses, even the winner. Eventually, such environment builds resentment and people will train hard so that they can topple the top dog, which defeats the purpose of training altogether.
Even if you come around and shake hands, hugs and all, there is still a level of distrust and guardedness which will not be conducive for mutually beneficial learning and advancement. Everyone will be watching everyone and I wouldn’t want to teach you my mat tactics; in the event I meet you on the mat, you will use what you learned about me, against me.

So yielding, or not; is a judgement call on the mat, and it takes years to discern how to compromise and how to stand firm. Sometimes it can be frustrating to learn that you cannot execute a specific technique against one specific guy in the dojo, then that is a sign you need to train more with that difficult guy, because your greatest lessons awaits.