Does it takes longer to cycle a route with a mountain on it comparing to the same distance without a mountain? What is the cause of that? Imagine you cycle 100km. On one route there is a mountain 100meter high on an other route is not a mountain but a straight way.

Usually it takes longer on the route wiht a mountain. One reason for that is that the time you spend going up the mountain is far more longer than going down. So at average you will go slower.

But how is it possible that with a moutain where the advantage of going downwards is equal to the disadvantage of going upward, at least regarding the objective obstacle.

Perhaps has something to do with the human body, but I can't see how this works.
Say you can keep a 30 kph pace on a flat straightaway. On a hill, that can drop to 10 kph or even less depending on the grade you have to climb. Call it 1/3 of your flat pace. Say that half your run is uphill and the other half downhill, and let's also say that the total run is 30 km.

If you run on the flat at your regular pace, it takes one hour to do that run. But if you do 15 km of the run at 10 kph, you'll spend 1.5 hours just going uphill. There's no way you can make up the time, because you're already over by half an hour. 

Now let's say you go uphill for only 10 km and downhill for 20. You still have only reached the summit when the hour's up.

There's a point at which you can do a short climb and still compensate by speeding downhill, but often you would have to attempt dangerous downhill speeds to make up your lost time. It's just not worth it. What is the obsession with time, anyway? In a race, everyone runs the same course.

Take comfort in the fact that the climbs you do are working your body much harder than running on the flats (or, obviously, downhill).