The fact that it is true is an experimental and observational fact.
So what you should ask yourself, is:
What assumptions have you made that precluded this experimental possibility?
Then you need to stop making that assumption so that you can open your mind to the way the world actually is, rather than how you thought it should be.
And the kinds of things you will need to throw away are.
- Two observers agree on how long an object is
- Two observers agree how much space separates two events
- Two observers agree how much time passed between two events
- Two observers agree on whether two events happened at the same time
- Two observers agree on which of two events happened first
When you abandon those kinds of assumptions you can consider lots of possibilities. And some of those possibilities include ones that agree with observation.
The point of physics is to agree with observation, not to agree with assumptions.
So if observer 1 thinks that event two events are a light speed apart, e.g. $(t_1,x_1)$ and $(t_2,x_2)=\left(t_2,x_1\pm c(t_2-t_1)\right).$ Then another observer, observer two, must also think that, e.g. $(t_1',x_1')$ and $(t_2',x_2')=\left(t_2',x_1'\pm c(t_2'-t_1')\right).$ This tells us how times and locations must appear differently to different people. We use things like that instead of assumptions (which is really just a kind of prejudice against theories). Then you can make theories where light speed is the same to everyone.
Then you can use such a theory to make predictions.
Then you can compare such predictions to observations.
And when you do you find they agree. And you find the Newtonian/Galilean type theories do not agree.