As I read the other answers, I find them all to make sense and be correct. Unfortunately, our friend still doesn't seem to grasp them, so I'm going to try to say the same thing (I feel it's correct) from a different approach.
If you take a picture of someone at night time, you might need a flash. This spits out a bunch of light that can get reflected off your subject and captured by your camera. But if you take the same picture of someone in the day time, there's a good chance you won't need the flash: there's already plenty of light floating around for your camera to capture.
Well, that's the same thing going on in space: there's a lot of light floating around. It's going to float around whether or not a camera is there to capture it. It's just going to go outward from the star or quasar or whatever produced it, and it's going to keep going until it runs into something. Maybe it runs into something close to what produced it. (Light from our sun does this when it hits us, we're pretty close.) Or maybe it runs into something super far away, like on the other side of the universe.
The key is that the light is already there. That's why we put the camera there. To capture the light that's already just kinda floating there.
Your 26 billion year scenario could make some sense: if we wanted to shine a "flash" at our target, flooding it with light to see what bounces back to us so we get a clearer picture, we could do that, and it would indeed take 26 billion years. (Probably longer, since it's probably accelerating away from us.) Well, in theory we could. The flash we made would probably be powerful to incinerate the earth, but that's a small price to pay to give some quasar its own selfie, right? We just have to hope we get it developed in time.