"Armor" isn't a function, it's only one variable. Graph armor rating vs damage reduction and what you get is a graph of diminishing returns, a logarithmic function. Graph armor rating vs life expectancy and you get an evenly sloping line. There is no need for you to "correct" what I wrote, because it was correct to begin with. Armor does have diminishing returns. Resilience needs to have the same or similar behavior.
The returns don't diminish though. If you go the route of saying armor has DR than all linear stats have DR, 1 Str provides less damage percentage at 20000 Str than it does at 2000 Str. The idea of diminishing returns is that you get less benefit as you increase how much you have. You get the same benefit from armor regardless of your current armor.
No, you're mixing together relative and absolute terms.
Strength gives the same absolute benefit at all levels of strength, assuming all other things are equal. If one point of strength is going to provide 10 DPS, then two points of strength will provide 20 DPS, and so on until infinity. The slope will remain constant (in this case, 10) forever.
Armor value literally provides less absolute benefit as it increases. Graph armor vs damage reduction, and it won't be a line with a constant slope. The slope will actually decrease as X approaches infinity, possibly becoming zero at some finite value of X.
What you're thinking of (I hope) is some thing more like Armor value vs Survival time in seconds. In that case, armor provides a linear benefit. So it is possible to say that armor provides a linear benefit (it depends what you define as the intended benefit) but it ALSO can be said to provide diminishing benefits (again, depending on what you define as the intended benefit).
Hence, your statement that "armor is linear" can be true, but my statement that "armor is dimishing" is not false. AND armor is not linear in the same sense that Strength is linear. Armor is linear in a relative sense and diminishing in an absolute sense, Strength is linear in an absolute sense and diminishing in a relative sense. Resilience is linear in an absolute sense, but geometic in a relative sense.
So no matter what, if you do an apples to apples comparison (relative vs relative or absolute vs absolute) all three of those functions will have a different shape from the others.
The bottom line, once again, is that resilience needs to have the same general behavior that armor rating has, for the same reason that armor rating was designed to work the way that it does: Otherwise you either hit a cap where the value of additional rating is zero, or it scales to the point where players become impossible to kill.