Why can't you remember falling asleep?

It's not uncommon for people to not remember their dreams.

Dreaming is actually a "byproduct" of the way that your brain processes information.

When you are awake, things that you are learning are stored chemically in the brain. When you sleep, the brain processes those chemical memories and forms permanent memories by generating new synapses. Dreaming can be part of the process of your brain "testing" these new synaptic connections.

The reason people cannot remember dreams is generally due to sound sleep; if you do not awaken during or shortly after a dream occurs, you mind does not transfer the awareness of that dream from short-term to long-term memory.

One method of remembering a few dreams is to set an alarm clock to awaken you several times during your normal sleeping period. When you awaken with thoughts of a dream in your mind, immediately record those thoughts on paper without getting out of bed. Such snippets of dreams are not likely to make much sense once you are fully awake, but they will provide evidence that you do, indeed, dream while sleeping, whether you remember those dreams or not.