Not thinking about, as much as observing the current sensations.
> why is focusing on breathing the only way that meditation teaches?
It isn't. You can focus on whatever you like, and there are descriptions of using pretty much anything you can think of as meditation objects. What you focus on is not the most important part, but that you focus your attention and your ability to go of thoughts.
Breath is often recommended because it is always available (takes away the excuse of "oh, I can't mediate because I need X and I don't have it here"), it is simple yet it has many qualities for you to observe; it has distinct phases (in-out) that are cyclical, and that have distinct pauses (when you shift from breathing in to out). It also has the property that it calms as you get more relaxed and more concentrated, so that the more you focus, the more you have to focus to keep attention on the breath.
At the same time, as you get deep into concentration, the fact that the breath calms lets you (if that is your goal) more easily shift the breath into the background, to focus on other things (e.g. your emotional state; observing fleeting thoughts; other bodily sensations or whatever else).
For a lot of forms of meditation, focusing on the breath is considered an important part developing "access concentration", that is, your ability to easily and rapidly calm yourself and enter into sufficiently deep concentration to focus on your desired meditation object.
For vipassana / mindfulness meditation, for example, the goal is not to endlessly focus on the breath, but to observe various aspects of reality (including the breath, but not limited to it) in a "detached" state where you are not engaging or reacting to them but simply paying attention to them. E.g. notice a thought arising, notice how your body reacts to it, but don't "respond" to it with a new thought - just observe the qualities of it, until it fades, and wait for the next one.
Meditating on breath then is a method of getting into deep enough concentration to enable you to do that without constantly "waking up" to realise you got caught up in some strand of thinking and spent the last 10 minutes thinking about what to do about your taxes.
(You can certainly observe the breath as the focus of your mindfulness meditation, but if you limit yourself to the breath you are
When I meditate, I usually notice my feet, for example. I notice my feet if I get a little bit jittery, and for me that's sufficient to cut a lot of the whammy out of strong emotion, agitation, moderate amounts of panic, pain.
I haven't noticed increased concentration skills, except as could be wholly explained by learning the skill "calm down on demand", but I'm not willing to write off that as a possibility without testing (a little late for me to test on myself, anyway!)
> why is focusing on breathing the only way that meditation teaches?
It isn't. You can focus on whatever you like, and there are descriptions of using pretty much anything you can think of as meditation objects. What you focus on is not the most important part, but that you focus your attention and your ability to go of thoughts.
Breath is often recommended because it is always available (takes away the excuse of "oh, I can't mediate because I need X and I don't have it here"), it is simple yet it has many qualities for you to observe; it has distinct phases (in-out) that are cyclical, and that have distinct pauses (when you shift from breathing in to out). It also has the property that it calms as you get more relaxed and more concentrated, so that the more you focus, the more you have to focus to keep attention on the breath.
At the same time, as you get deep into concentration, the fact that the breath calms lets you (if that is your goal) more easily shift the breath into the background, to focus on other things (e.g. your emotional state; observing fleeting thoughts; other bodily sensations or whatever else).
For a lot of forms of meditation, focusing on the breath is considered an important part developing "access concentration", that is, your ability to easily and rapidly calm yourself and enter into sufficiently deep concentration to focus on your desired meditation object.
For vipassana / mindfulness meditation, for example, the goal is not to endlessly focus on the breath, but to observe various aspects of reality (including the breath, but not limited to it) in a "detached" state where you are not engaging or reacting to them but simply paying attention to them. E.g. notice a thought arising, notice how your body reacts to it, but don't "respond" to it with a new thought - just observe the qualities of it, until it fades, and wait for the next one.
Meditating on breath then is a method of getting into deep enough concentration to enable you to do that without constantly "waking up" to realise you got caught up in some strand of thinking and spent the last 10 minutes thinking about what to do about your taxes.
(You can certainly observe the breath as the focus of your mindfulness meditation, but if you limit yourself to the breath you are