People who brag about not caring usually care the most about you noticing.

Announcing indifference requires an audience, which gives the whole thing away. If something genuinely did not matter to you, there would be no reason to bring it up, and the effort of making sure everyone knows you are unbothered is itself the caring. It is usually armor rather than dishonesty.

When someone does this near you, resist the urge to point it out, because it never lands well. Just do not take the performance as information. And notice when you are doing it yourself, which is usually right after something got to you more than you would like.