Someone calculates the 95% confidence interval for the average weight of teenagers by collecting data from a simple random sample of 100 teenagers. Circle the correct interpretation(s) of the confidence interval (there may be more than one correct answer): 1) There is a 95% chance that the average weight of all teenagers falls in this range. 2) There is a 95% chance that the interval created includes the average weight of all teenagers.

Step 1
On the face of it, “the average weight of all teenagers falls in this range” and “the interval created includes the average weight of all teenagers” indeed mean the same thing, just as $x\in <!--\; \in \; -->[0,1]$ and $[0,1]\ni <!--\; \ni \; -->x$ mean the same thing and $A\subset <!--\; \subset \; -->S$ and $S\supset <!--\; \supset \; -->A$ mean the same thing. So if this is a test, it’s a rather badly formulated one.
Nevertheless, it’s true that there’s a subtle difference here that’s related to the difference between the frequentist and Bayesian paradigms. “You ate the apple” and “The apple was eaten by you” also mean the same thing, but they focus on different aspects of the situation – your agency and the fate of the apple, respectively. It's more natural to say “You should be punished because you ate the apple” than “You should be punished because the apple was eaten by you”, because conventional concepts of punishment are linked to agency. “2 plus 2 is 4” and “4 is 2 plus 2” also mean the same thing, but while there are contexts where the one or the other is appropriate, there are few contexts in which both are appropriate - again because they focus on different things – the result of an operation and the possibility of decomposition, respectively.
Because in “the average weight of all teenagers falls in this range”, the average weight is the subject of the verb “falls”, which is associated with randomness, this formulation sounds as if (or at least could be interpreted to mean that) the average weight is a random quantity that in this case falls in this range but in other cases, when the experiment is repeated, might not fall in this range. By contrast, in “the interval created includes the average weight of all teenagers”, the interval is the subject, and thus it’s the interval that has possible “agency” in the sense of having the option of doing or being something else – if we repeat the experiment, we might get a different interval, and then the interval not including the average weight would be the interval’s “fault”, not the average weight’s.
Step 2
Thus, in the frequentist paradigm, where the average weight is treated as a fixed (though unknown) quantity, it's more natural and in a sense more appropriate to say “the interval created includes the average weight of all teenagers” than “the average weight of all teenagers falls in this range”. It does a better job of implying that if we were to repeat the experiment, it's the interval that would change and not the average weight.