Imagine that you took a video picture of the hiker on the way up and a separate video of the hiker on the way done. Now superimpose the two videos, both starting and ending at the same time. Since the hike up and the hike down follow the same path, the superimposed videos will show the two hikers crossing at some point. That's the point where the hiker reaches at the same time on the way up as on the way down.