Approximating the Earth by a circle with West facing in the theta-hat direction and East in the opposite, when a person jumps up, the Coriolis force faces West according to the right-hand rule. Upon descent, the Coriolis force faces East. Since you spend an equal amount of time rising and falling, shouldn't the effects of the Coriolis force cancel out? Why is this not the case? Why does a person end up falling slightly West?
There is a fallacy in your reasoning.
The ascent begins exactly vertically. Because in the ascent phase the Coriolis force points to West, at the peak you will have a small horizontal velocity pointing to West. Then, in the descent phase the Coriolis force points to East. So when you hit the ground again, the horizontal velocity will come back to zero (meaning you hit the ground exactly vertically).
So, regarding horizontal velocity, the Coriolis effects from ascent and descent phase indeed cancel out. But the effects do not cancel out regarding horizontal position.
Obviously, during ascent and descent phase the horizontal velocity always points to West (except for the start time and end time, when the horizontal velocity is zero). Therefore you get a westward displacement in position between start and end.