What I am - an animal (may be)?

Maybe you are

People call me an animal

Since I possess a tail

but it's in the opposite direction.

I can't travel beyond some point

Since I am bound by my tail.

Sometimes I don't have a tail

But still I can not travel that far.

Go to the right and world is easy for you.

Go to the left and change your mode.

You touch me often, but I won't bite you.

The correct answer has been posted, but this was my initial guess.

I think you are:

People call me an animal

Since I possess a tail

but its in opposite direction.

I cant travel beyond some point

Since i am bound by my tail.

Sometimes I don't have a tail

But still I can not travel that far.

Go to right and world is easy for you.

Go to left and change your mode.

You touch me often, but I won't bite you.