Keep in mind that these are very crude generalizations about stall progression on wings. Two different elliptical wings will stall differently due to differences in the airfoil, and protrusions on the wings such as pitot tubes, landing lights, etc..

The reason that straight, untapered wings stall at the root first is because of the tip vortices and fuselage interference, as mentioned before. The air circulation around the tip decreases the angle-of-attack at the tip of the wing, which actually influences the flow around the rest of the wing.

The reason the stall will tend to start at the tip on highly tapered wings has to do with relative Reynolds Number between the root and the tip. The shorter the chord, the lower the Reynolds Number. Most airfoils will stall at a lower angle-of-attack at lower Reynolds Numbers.

The reason the stall will tend to start at the tip on highly swept wings is because of the spanwise flow on the wing. Aft wing sweep induces outward spanwise flow (toward the tip). The opposite is true on forward swept wings.

Also, there are ways to fix stall progressions that begin at the tip by varying the airfoil shape along the span, adding wing twist, leading-edge slats, fences, etc..