Is it normal that i'm afraid of ceiling fans?

With the fan off... Stand on a chair or stool and reach up and see if you can wiggle the base mount of the fan.

If it's solid it won't likely fall down.

If it's loose, ask the owner to fix it.

I installed ceiling fans in my house (replacing existing light fixtures). They are very solidly mounted.

I also have the kind without the strings. Controlled with a light and fan controller box that replaced the old light switch (that's a premium priced fan - but well worth it).

check yours for loose screws and see if the mount is hung tightly

find someone who installs em and participate in a correct & safe install to see what it takes

theres some definite measures to be taken for safe setup but its really no big deal to do it right

I use to worry about that as a kid. You would survive almost certainly. But itd be a shitty wakeup.

It's not a completely irrational fear. Anything mounted on the ceiling can fall if it wasn't installed correctly. Olderdude and donteat have suggested how you can check if it's secure.

You might want to consider carefully wiping down the fan blades periodically. The blades are balanced to minimise vibration, and the accumulation of dust on them can cause shaking. This could conceivably pull the fixing screws free over the long-term if they weren't firmly attached to something solid under the surface of the ceiling. Keeping the blades dust-free also minimises the noise of the fan.

Some other points you might bear in mind: Ceiling fans generally aren't very heavy; they're just a small electrical motor in a lightweight housing attached to flimsy blades, and those blades aren't razor-sharp. If a ceiling fan were to fall right on your head, I'm sure it would hurt, but it's extremely unlikely that you'd be seriously injured. Also, ceiling fans have to be connected to the household wiring, so if the mounting were to fail, it's possible the fan would just end up dangling from the wiring.