Could be because "go climbing" is used in the same way as "hiking". Simply saying "climb" might be too general since this only means climb a mountain. It should be accepted but it's better for them to just say hiking instead.
Why 다시 등산합시다" (Let's go HIKING again) was translated with the present continuous form of the verb "hiking".
However "함께 등산합시다" was translated with the present simple form. "Let's HIKE together"
I didn't understand. Someone can explain to me?