I can make pigs fly

Question

I slip through your fingers as sand in a sieve,
A brief moment, an eternity, is when I live.

Maybe I'll drown you, or give you flight,
Some say I fill you with both terror and delight,

Let us not forget, my most memorable feature,
Each time you see me, I become a preacher.

Even though it seems, I make the impossible happen,
Perhaps you should listen, instead of just napping.

Your true self I show, in a puzzle like this.

Answer 1

You are:

dreams.

I slip through your fingers as sand in a sieve,
A brief moment, an eternity, is when I live.

When you wake up, it may feel like you just went to sleep moments earlier, even if it's been hours, or it may feel like you've been asleep for forty years.
Dreams may mess with one's perception of time; it's possible to have dreams that seem to take place over several days in a single night.

Maybe I'll drown you, or give you flight,
Some say I fill you with both terror and delight,

Drowning and flying are both common motifs in dreams. Dreams/nightmares may be fun or they may be scary.

Let us not forget, my most memorable feature,
Each time you see me, I become a preacher.

I'm less certain on this one. Some religions ascribe religious significance to dreams, hence preaching. Jungian psychology says that recurring dreams may have a purpose that the waking person must fulfill to stop them.

Even though it seems, I make the impossible happen,
Perhaps you should listen, instead of just napping.

In dreams, the rules of reality may no longer apply. Napping references to sleep and light dreaming directly. This is where the title applies: only in dreams can something impossible happen, like seeing pigs fly.

Your true self I show, in a puzzle like this.

Dreams may be said to show 'your true self' without conscious inhibitions. Also, note that the first letters of each line in order spell, "I AM SLEEPY"