Wrong. It's all relevant. Equal and opposite reaction to action.
That doesn't magically make it relevant as you are yet to show any involvement of the external atmosphere in any action or reaction.
Again, why isn't the action/reaction contained inside the vessel?
Just think of that box full of water and picture the people in it.
You can understand that everything in that water is displacing it.
However to allow those people and see saw in, you have to eject their entire mass of it back out.
Which is entirely irrelevant to the discussion as the people and see-saw are already in. We aren't sticking them in again.
Them moving around doesn't magically mean the water needs to get thrown out again.
Deal with the movement once they are already in. That means no extra pressure because we aren't trying to force air out, just move it around.
There is no problem. The problem is all down to you not understanding it.
The problem is not us not understanding it.
The problem is you not having an explanation which can withstand any scrutiny and instead you repeatedly deflect.
You have been completely unable to explain why the atmosphere pushes down, except in the cases where you contradict yourself and say it pushes up.
The closest you have come is saying that if you are in the atmosphere, you push it out of the way and compress it all around you, except for below. You have failed to provide any explanation for why the atmosphere below isn't compressed and instead just happily sits there to not provide any force to you.
So no, the problem is entirely you and your model.
Take a steel ball attached to a chain and hang it from a spring balance.
Note the weight.
Then submerge it in water.
Note the weight.
We observe the weight of the steel ball is reduced, even though it sinks in the water.
So we know that buoyancy is not a magical change where an object magically starts floating because of some magical resistance nonsense and instead is a force that acts on any object in any fluid.
Here is a video for you:
First of all the steel ball displaces a lot of atmosphere and that same ball is using a spring as it's resistance and also the water as it's much denser foundation than the atmosphere it would be hanging in.
It can displace that atmosphere much easier than it can displace that water...hence why the spring will register less weight measurement of that mass due to that resistance of water.
And more pathetic deflection.
You asked for an example of an object weighing less while still sinking.
I provided an example.
This shows that buoyancy is not just a magical resistance nonsense.
Were you hoping I wouldn't be able to provide such evidence?
It's all well and good to just spout all that nonsense, but it doesn't change the fact that this shows buoyancy acts on all objects, not just those less dense than the fluid they are in.
But yet again, you have contradicted yourself.
Isn't it all meant to be about action and reaction?
If it is harder to displace the water, that means it requires more action, and thus you should have a greater reaction, so the object should weigh more in water.
We can also test that it has absolutely nothing to do with how hard it is to displace the fluid by using fluids of differing viscosity.
It is much harder to move fluids with a greater viscosity out of the way, but the buoyant force observed is always based upon the density of the fluid, not the viscosity.
So it clearly has nothing to do with how hard it is to push it out of the way.
But more importantly, once the water is displaced, why should it matter? Displacing the water is a property of motion. Once it is in the water, and "stationary" it is no longer displacing the water. So why doesn't it have the full weight back?
It would only make sense for the difficulty to displace it to affect it when it is falling through it, not when it is stationary.
And going back to viscosity, that is what is observed. If you drop an object through a viscous fluid the rate it falls at depends highly upon the viscosity of the fluid as that effects the terminal velocity of it.
But that is just the velocity it falls at. Once it stops falling and you measure the weight, the weight depends on the density of the fluid, not the viscosity.
Care to try again?
Care to explain why the density of the fluid is what matters? That means no appealing to any resistance or how hard it is to displace that fluid.
And of course you ignore the problem you claimed you would stick to yet again.
Once more:
Why does the scale not record an increase in weight but the pressure gauge does record an increase in pressure?
And as you want to avoid so many issues and not stick to this one like you said you would, I may as well bring up the other issues you have been avoiding:
Why does an object in mid air get pushed down, even though it has air all around?
Why does a suction cup get pressed upwards to the ceiling rather than fall down if the air below doesn't push up?
Why only a suction cup rather than any old object?
Similarly, if it is based upon the ground being below you, why doesn't it apply a sideways force if you put yourself up against a cliff?
Why does the pressure/weight/force increase as you move down a stack, if all the force is being applied from the top?
Why does a barometer work, with it working depending on its orientation?
Why does a vessel weigh less if you evacuate the air from it, i.e. cause it to displace more air?
Why does the weight of an object depend upon its mass, rather than its volume or cross sectional area, when all forces of air and other fluids and observed to be proportional to area, not mass?
If air can magically penetrate through everything such that the "volume" an object displaces is magically proportional to its mass rather than being its actual volume, how is anything air tight?
If weight is based upon displacing atmosphere with that atmosphere pushing back onto the object with an "equal and opposite reaction", how come when you replace the atmosphere with a denser fluid, how come the weight becomes less rather than more?
Likewise, why, when you lower the air pressure (making it easier to displace the air), the weight of an object increases, rather than decreases, but only to a point, where when the object is in a near perfect vacuum, with effectively no resistance from the air, it still has a significant weight rather than being weightless?
And the more fundamental issue, why does air stack in the first place?
They are the ones I can remember off the top of my head. There are probably plenty of others I have forgotten for now.