Background removal without a green screen is an underdetermined problem. Here's what the maths is doing.

Every pixel in a photograph of a person against a wall is a blend of two things. The compositing equation is the whole problem in one line:

C = αF + (1 - α)B

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C is the pixel you can see. F is the foreground colour, B is the background colour, and α is how much of that pixel belongs to the foreground. Solid shirt, α is 1. Empty wall, α is 0. A single strand of hair crossing that pixel, α is 0.3 and the pixel is genuinely part person, part wall.