Why doesn't my projector recognize the PC via a switch?

As written above, I have the problem that my projector does not recognize the connected switch with pc. It is not because of the cables that they work otherwise. The switch itself works, e.g. Works With Playstation 4. The PC itself also works with the projector, but only as long as there's no switch in between. Is the switch in between then the PC recognizes the projector, just not the other way round… Any idea what I can do? Respectively. Maybe there could be a defect?

Perhaps the switch does not "switch" all the wires of the cable.