Not to be confused with Double tapping.
Alternating is a tapping style for osu! in which players click circles, slide sliders, and spin spinners by alternating between two set keys on their keyboard (Z and X by default) every other hit object or so. Hence the name. This style is most common amongst more seasoned players and is one of the hardest to adapt to.
Alternating has a wide variety of uses and its forms can vary from player to player. For example, many players who alternate typically switch between Z and X on every other note (or hit object), while others switch keys after every two to three hit objects. It should be noted that some players will alternate most of the time, but sometimes hit the same key twice if a hit object catches them off-guard. This is all simply down to personal preference.
On a similar note, some players prefer to tap their keys using the index and middle finger, while others use their index and ring finger. Index and ring finger players will typically have their keys set farther apart to accommodate for the larger gap. E.g., Z and C as opposed to Z and X.
Arguments in favour of alternating typically mention that alternating is much faster as it reduces the amount of time between keypresses as opposed to single-tapping and that it gives time for each finger to rest and thus allows players to play faster for longer.
Arguments against alternating typically mention that it is much harder to keep consistent because one finger is usually stronger/faster than the other, while others argue that alternating can cause confusion on faster, more intense levels.