Sure you are. You say the correct location for the light is the one which the prime frame measures, and you claim the other location for the light (which is the one which the unprimed frame measures) is incorrect. You are unwittingly choosing the primed frame as the preferred frame.
Here, let me show you your argument in a Minkowski diagram:
You are arguing that since the co-location of C' and M occurs at $$t'=1.000$$ then the correct location of the light must be $$x'=1.000$$, and the other event which shows the light located at $$x'=0.500$$ is just a byproduct of SR randomly generating incorrect coordinates.
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Now let's look at a different Minkowski diagram:
Based on your logic, since the co-location of C' and M occurs at $$t=0.866$$ then the correct location of the light must be $$x=0.866$$, and the other event which shows the light located at $$x=1.732$$ is SR randomly generating incorrect coordinates.
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But guess what? Those two diagrams are just different ways of drawing the same events:
Now do you get it? The answer you claim is wrong can be justified the same way as the answer you claim is correct. Did you forget that SR taught you that all inertial frames are equally valid? Now don't you feel silly?
Here is specifically where you failed. The OP asked where is the light in the coordinates of the primed frame. Now, if SR is a consistent theory that works, it will give the correct answer. This is very simple.
So, if C' and M are co-located, SR gives 2 answers on the location of the light flash. Naturally, we can quote ROS and say events in one frame that are simultaneous are not in another.
That is all fine and good. But, the OP asked a very specific question, where is the light in primed frame measurements if C' and M are co-located,.
Unfortunately, SR claims it is at 2 places as the math in the OP demonstrates.
See, here is your task. You need to prove SR says it is at one place since there is only one beam of light if C' and M are co-located.
Therefore, you have confessed, if C' and M are co-located, then SR claims the light is at 2 different locations in primed frame coordinates, which contradicts nature.