TL;DR
Longer methods are more likely to need to change when the application changes.

The Longer Story
Shorter methods protect my investment in the code, in a number of ways.

First: Testability. I expect there to be a correlation between method length (number of “statements”) and the number of (unit) test cases required to validate the method completely. In fact, as method size increases I expect the number of test cases to increase faster than linearly, in general. Thus, breaking a large method into smaller independent methods means I can test parts of my application’s behaviour independently of each other, and probably with fewer tests. All of which means I will have to invest less in creating and running the tests for a group of small methods, compared to the investment required in a large method.

Second: Cohesion. I expect there to be a strong correlation between method length and the number of unknown future requirements demanding that method to change. Thus, the investment I make in developing and testing a small method will be repaid countless times, because I will have fewer reasons in the future to break it open and undo what I did. Smaller methods are more likely to “stabilize out” and drop out of the application’s overall churn.

Third: Coupling (DRY). I expect that longer methods are more likely to duplicate the knowledge or logic found elsewhere in the same codebase. Which means, again, that the effort I invest in getting this (long) method correct could be lost if ever any of those duplicated pieces of knowledge has to change.

And finally: Understandability. A method that does very little is likely to require fewer mental gymnastics to fully understand, compared to a longer method. I am less likely to need to invest significant amounts of time on each occasion I encounter it.

The Open-Closed Principle says that we should endeavour to design our applications such that new features can be added without the need to change existing code — because that state protects the investment we’ve made in that existing, working code, and removes the risk of breaking it if we were to open it up and change it. Maybe it’s also worth thinking of the OCP as applying equally to methods.