Why does one get an illusion as moon following him? When you run or ride bike at night if you observe the moon you feel like he moves along with you as the same speed you are going. Why?
 A: Suppose you're walking past a nearby tree:

As you pass the tree the angle of the line joining you and the tree changes. From your perspective it looks as if you are standing still and the tree has moved backwards.
However the Moon is so far away that, as you walk, the angle of the line joining you to the Moon doesn't change by any significant amount:

So, from your perspective it looks as if the moon is keeping up with you i.e. it's traveling at the same speed as you are.
This effect is particularly marked if there are any nearby landmarks. For example, nearby trees seem to move backwards as you pass them, and this enhances the feeling that the Moon is moving forwards to keep up with you.
A: The moon is a lot further away than the horizon or nearby buildings, trees, hills or mountains.
As you pass these nearby objects, from your perspective you see them apparently move backwards relative to your motion. 
This is a matter of simple trigonometry.
This is because, the angle between your bicycle and (for example) a tree 100 metres away changes noticeably when you move forward 10 metres.
The change in angle for the moon 384,400,000 metres away is imperceptible.
This is an example of parallax


For a very distant object, such as the moon, $\alpha$ will be almost zero
