Intuition is definitely subjective, and that is ok. I do respect different intuitions while trying to understand them. And the best thing for that is doing what

Intuition is definitely subjective, and that is ok. I do respect different intuitions while trying to understand them. And the best thing for that is doing what you did, which is provide a more clear example. Unfortunately, the example makes it more clear to me that probability differences are linear. Your "difference of log-odds" function is a qualitative function that you've constructed to operate on probabilities. All you've done is take the log of numbers and compare them, and of course you're going to take on the properties of logarithms themselves: specifically that the difference between log(x2) and log(x1) decreases as x2 and x1 increase in value. That's just how logarithms work. This says nothing about the relationship between probabilities. You can't just apply any operation on any values and draw conclusions about it with understanding the interpretations of the values. Probabilities are likelihoods, not raw quantities. So the domain of likelihood has to be considered when analyzing probability values. In the domain of likelihood, when probabilities are independent (i.e. flipping a coin once does not influence the next coin flip) you can interpret differences in probability as linear.