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Separate object from background best procedure

I have two photos that were taken in a burst (the movement between the two is very small, exploiting the hand jitters between the two images), and I have to use the two to suppress the background and separate the wanted object from the background. The user of the app presses on the object to separate.

I tried using SGBM to find the depth map, and then I could threshold the values close to the values in the point the user pressed, but the results are horrible (no matter the parameters chosen - my guess is that is because the images are not exactly left-right versions of the same scene, but slightly lowered and heightened as well).

Example for using SGBM for a slightly tilted pair of chair images

What is the best course of action to do what I need? I have to use a pair of very close images, which are randomly tilted from each other. Is the fact that the images are so close to each other problematic? I tried everything I can but nothing works.