Why do you forget your dreams so fast?

Dream forgetting is not a failure of recall so much as an absence of encoding. During REM sleep, when most vivid dreaming occurs, the brain's neurochemical state changes markedly: noradrenaline, which plays an important role in forming lasting memories, drops to very low levels, and the hippocampus, central to converting experience into durable memory, is operating in a different mode oriented toward consolidating the day's existing memories rather than recording new ones. So the dream is experienced without being written down in the usual way, which is why it dissolves within minutes of waking even when it felt vivid.

There is also a retrieval component. Dream memories, when they do form, are fragile and highly dependent on context, and the shift from sleep to wakefulness disrupts the cues needed to access them. This is why moving your body or checking your phone on waking often erases a dream you briefly held, and why lying still and recalling before moving improves retention noticeably. People who wake naturally during or just after REM remember more, which is partly why dreams recalled are disproportionately from the final sleep cycles before waking. Keeping a notebook and writing immediately measurably increases recall over time, apparently by training attention toward it. Individual variation is large, and low dream recall is not a sign of any problem, since everyone dreams roughly the same amount regardless of what they remember.