I've prepared a simple toy:

It consists of a pencil and a string that goes through a hole in the pencil and makes a loop. The ends of the string are glued together. 

The loop is shorter than the long end of the pencil:

so, it can't be moved over it.

Then, I insert the pencil through the buttonhole like this:

This is how it looks from the other side:

I can separate them again and repeat without cutting, breaking, untying, etc.

Can you figure it out?

I can take more pictures, from different angles, if you need. There are no hidden cuts or anything like it. You can make it yourself.

 

 

This is what happens if the pencil is pulled to the right:

and to the left:

How to get it out?

Reminder:

Spoiler

We live in a three-dimensional space.

 

Spoiler

When you pulled to the left, you essentially made a knot.  To untie, you don't stretch the string, but rather stretch the fabric in three-space, as you reverse the original knot.  

 

Good! +1

And,

Spoiler

it can be easily solved when you pull to the right. Do you see it?

 

Spoiler

Except for a different parts orientation, taking the pencil off the buttonhole is not different from unbuckling a belt: