You are right  if they are dangerous predators present and have been seen in
your area  than it is pretty stupid of your parents not to take it serious

Second if this is a kitten  why would they want to put it in danger by
introducing it to the outside world  there are so many dangers out there.
they have to think of this kitten as a small child

If they are worried about sleep  keep it in your room at night

A cat or kitten that is an outside animal they don't just stay in your yard
they wander just like all animals that are outside do.  While living happily
inside, cats are not getting hit by cars, being injured in cat fights,
catching infections such as feline leukemia virus and feline
immunodeficiency virus (Feline "AIDS"), being stolen, hunting and possibly
killing wildlife, urinating and defecating on neighbors' properties, and
harassing or being harassed by other animals.

Personally IMO if your parents  aren't listening to you about possible
dangers and health factors than they are being pretty selfious and you can
truly see how they are in life

Read below from a professional if this doesn't convince them  than they will
never listen
http://www.maxshouse.com/Healthy+Happy_Indoors.htm#Inside%20or%20Out

Hello Everybody,

When I first got my kitten 2 months ago, I wanted her to be a indoor cat. My
mother (Who lives with me) wants her to be an indoor and outdoor cat. The
problem is that there are coyotes in my area (Even though I live in the
city, I have seen coyotes roaming in the city).

But my mother nor my father doesn't take this serious. To their mind, they
want my kitten outdoors so that she would sleep at night. Another point that
they are not thinking about is that cats are night hunters. We do put her in
her crate so that my kitten wouldn't have to wake us up in the middle of the
night biting us in the leg or playing with our hair.

Here is another thing that my parents are not thinking about. Yes, my kitten
follows everyone around in the house. There was one time where she was
outside and my father was out looking after the yard. Mind you when they
were looking for my kitten, it took awhile to find her (I can't remember
where they found her). But, what if they did turn their backs and my kitten
roamed off never to be seen again?

Who is right in this argument?

Around here many a cat has been killed by a wild animal.  

Here they advise keeping cat indoors to keep it safe from
predators.  

I am a 100% cats indoors kind of person.  That being said, I don't go
hitting people over the head to keep theirs inside.  I tell them of the
dangers, and of the accients (like the kitten I saw with a stick in its eye)
and the infectous diseases.

But those were pretty much touched upon in the other replies.

I suppose what really matters is who's house is it?  Is it yours?  Well then
throw the ol "While you are living under my roof you'll live with my rules"
thing.  :)  If you want your kitten indoors, then that is how it is going to
be if you are paying the rent.

If it is a 50/50 thing, or if it is their house, you'll need to be more
creative.

As for the sleeping at night cause it is outside arguement, that is a
fallicy.   I have seen many a cat sleeping outside.  Kittens need a ton of
sleep, but not all at the same time, so as a kitten, no matter what you do
it is going to be awake in the middle of the night.  I have six cats who all
live in doors with me, and for the most part they let me get a full nights
sleep.  And if you don't let the kitten run around at night and bite your
toes and learn that is wrong, you'll have an adult cat that will do that,
and their bite is a lot worse than a kitten.

You could implement play time right before you go to bed to wear the kitten
out and so it won't feel so attention starved when you are sleeping.  A nice
fishing pole type of toy will get her running all around and work out her
hunting skills :)  Cats hunt at dusk and dawn.  That is what their eyes were
designed for.  Those low light times.  They can't see in the absence of
light.

Good luck!

Hello Everybody,

When I first got my kitten 2 months ago, I wanted her to be a indoor cat. My
mother (Who lives with me) wants her to be an indoor and outdoor cat. The
problem is that there are coyotes in my area (Even though I live in the
city, I have seen coyotes roaming in the city).

But my mother nor my father doesn't take this serious. To their mind, they
want my kitten outdoors so that she would sleep at night. Another point that
they are not thinking about is that cats are night hunters. We do put her in
her crate so that my kitten wouldn't have to wake us up in the middle of the
night biting us in the leg or playing with our hair.

Here is another thing that my parents are not thinking about. Yes, my kitten
follows everyone around in the house. There was one time where she was
outside and my father was out looking after the yard. Mind you when they
were looking for my kitten, it took awhile to find her (I can't remember
where they found her). But, what if they did turn their backs and my kitten
roamed off never to be seen again?

Who is right in this argument?

Is this a joke?  If it is really your house and they live with you,
then you get to make the rules.  If it's their house, then they make
the rules.  Sounds like you have an innocent kitten in the middle of
you and your parents' power play.  

If you can't/won't provide a safe and secure home for the kitten, then
find someone who will.  Don't make the kitten pay with its life.