Where is the logical fallacy?

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Where is the logical fallacy?

In The Amer magazine. math. Monthly a task was placed, which in translation sounds like this: “from what point on the globe do you need to leave in order to walk 10 km along the meridian to the south, then 10 km along the parallel to the east, and finally, again 10 km along the meridian to the north, to arrive at the point of departure?”

One solution is almost very visible: exit the North Pole. Interestingly, this solution is not the only one. One prominent mathematician addressed this problem in this way. The first and third parts of the path pass along the meridians; but the two meridians have only two common points - the northern and southern stripes; the latter disappears, since it is impossible to move south from it; the northern lane remains as the only solution.

What is the reasoning for the error and how to get the complete solution?