Well, you try to build an idea based on your logic that in your mind, breaks the theory of relativity. But the thing is, it doesn't work that way. Our logic and intuition are wrong in so many ways, they really shouldn't be taken seriously.

Observations often lead to bad models about reality, because what we see is rarely what is. For example take two falling objects, we can see easily that heavy objects fall faster than light objects. That's very obvious and everybody agree on that, except… except that it is wrong, and “really” all objects fall at the same speed and in the same way because of the same cause. Only the air changes the fall characteristics.

So you don't need to invent some complicated “spaceship that travels close to the speed of light from which you throw something fast”, you just need to walk at 5 km/h (or any non-null speed) and turn on a flashlight. Then question: what is the absolute speed of light as seen from the floor? And what is the speed of light as seen from you, the moving source for light?