When you throw the hoop forward and add backspin at the same time, two separate motions exist at once: the hoop is translating forward (moving as a whole) and rotating backward (spinning in the opposite direction to its travel). At the single point where the hoop touches the floor, these two motions partially cancel — but the forward slide still wins initially, so the contact point is sliding forward against the floor.

Friction always acts to oppose sliding. Because the contact point slides forward, friction acts backward on the hoop. This backward friction force does two things simultaneously: it decelerates the hoop's forward motion, and it reinforces the backspin (adding rotational energy in the backward direction). The hoop slows. The backspin grows relatively stronger. Eventually, the forward motion reaches zero — but the spin is still there. With no forward motion left to oppose, the spin takes over completely and rolls the hoop backward — back toward you.

The critical insight is that friction here is not a passive resistive force — it is the active agent of reversal. On a frictionless surface (ice, for example), the spin would have no contact point to act through, and the hoop would simply travel forward until it fell over. Friction is what makes the spin matter. 

For a completely different role for the same force — where friction between wheels and floor is what prevents motion rather than creating it — see [Newton's Question: Who Moves?].

This is identical to the backspin draw shot in billiards: the cue ball slides forward, friction decelerates it, and the backspin eventually rolls it backward. Cricket bowlers use the same principle when applying spin to change a ball's direction after it pitches. 

Tennis players use backspin (slice) to make the ball stay low and slow on bounce. In every case, the mechanism is the same: friction at the contact surface converts rotational energy into a change in translational direction. For an experiment that uses an entirely different force to create surprising direction changes in air, see [The Impossible Blow].