They did it because they knew Oswald was going to deny owning the rifle, and they wanted to have a piece of tangible, visual evidence linking him to it.
But, they made a big, colossal huge mistake, and that was to show it to Oswald. What for? They didn't need to do that. They made it to show the world, not him. They should have waited until he was dead, and then, lo and behold, found the photos. That way, he never would have been able to renounce them. It would have just been him brandishing the murder weapon and Marina saying it was so. Of course, Marina would have said anything was so; whatever they wanted. I don't know how, but somehow, they flipped a switch in her brain that made her absorb every lie they were telling her and make it her own. And that is really the worst and most diabolical thing that happened after the assassination: the corrupting of Marina Nikolayevna Oswald. Talk about the devil's handiwork.
But, it is very significant that even after being shown the Backyard photo, Oswald continued to say, "I don't know anything about that rifle, and that is not me in the picture. It's fake."
I am reminded of a cop show in which they lured these offenders to a place by sending them a notice that they had won a contest and they needed to go there to collect their prize. So, this big cop gets up on the stage in front of all these highly expectant criminals and says, "Before we go any further, I need to tell you that I am Officer So-and-so, and you are all under arrest." Some of them were deadbeat dads. Some of them were wanted on warrants. No murderers. But, one guy was wanted because he had lost his license because of repeated drunk driving, and some concerned citizen sent the police a photograph of him driving. So, they told him why he was being arrested, and he tried to deny that he had been driving. Well, he admitted driving to get there, but he said that they put him up to it, and it was the only time he had done so. And that's when they showed him the photo. And then he shut up.
But, the point is that he didn't say that it wasn't him in the photo, that somebody had moved his face to the body of another driver. NOBODY WOULD DO THAT WHEN PRESENTED WITH A REAL PHOTO OF HIMSELF. It's not how the human mind reacts in that situation. Who would be so arrogant as to look at a real photo of himself- one that he knew he posed for- and say that it's fake? The fact that Oswald reacted that way proves that he really was sure it wasn't him and couldn't possibly be him- because he never posed for such a picture, and he didn't own that or any rifle.
I'm saying that if that were a real photo of him, the odds of Oswald lying about it in that manner are next to zero. Do you know anyone who has ever done that? I didn't think so.
This graphic is from Jim Fetzer and Jim Marrs, and they make a valid point: why should Oswald's face and expression be EXACTLY the same in subsequent pictures? People aren't automations. Here's the link to their excellent analysis which destroys the Backyard photos: