Why aren't the reviewer or steward badges shown or selectable as "next badge" on the user activity page? They are shown among the help-center badges.
Quite a few badges aren't in the tracking list. (There are about 15 badges I don't have but only 4 show up that I can choose between for tracking)
Some of those at least will probably be for reasons of overhead (it would be too hard to keep doing the calculation every time you load your profile).
Some will be absent because you don't really "progress" toward them.
Some will be absent because they're already shown elsewhere. The reviewer progress is shown in information under the "review" menu item / review queues (e.g. https://stats.stackexchange.com/review/close/stats shows close-reviewer badge progress, https://stats.stackexchange.com/review/suggested-edits/stats shows suggested-edit reviewer badge progress and so on)
So I expect that they don't show up because you're already getting a display that's "tracking" them elsewhere.
Note also, as suggested, I asked this question on SE meta, and the answer there was
These badges are intentionally not available in the badge progress selector because they would require additional UI to select which queue you wanted to track which is simply not worth implementing at this time given that you can easily track these in each queue respectively.