Individual functions may have a lot of different versions. They do only update them if there is an ABI change (so you may have e.g. f1_v1, f1_v2, f2_v2, f2_v3 as synbols in v3 of glibc) but there's no easy way to say 'give me v2 of every function'. If you compile against v3 you'll get f2_v3 and f1_v2 and so it won't work on v2.
Why are they changing? And I presume there must be disadvantages to staying on the old symbols, or else they wouldn’t be changing them—so what are those disadvantages?
Depends on the functions. One example is memcpy - the API specifies that the source and destination must not overlap but the original implementation in glibc didn't care. When they wanted to optimize the implementation they decided to introduce a new version of memcpy rather than breaking older binaries that inadvertently relied on on the existing behavior even if that was never guaranteed by the API. Old binaries keep getting the older but slower memcpy, new binaries get the optimized memcpy.
Other examples are keeping bug compatibility, when standards are revised to require incompatible behavior, or to introduce additional safety features that require additional (hidden) arguments automatically passed to functions which changes their ABI.
