The phrase "to climb down" means to admit defeat, back away from a position or demand, or change one's opinion or stance due to new evidence or circumstances. Full definition
Actually, it is and he had better climb down from that shaky pedestal. (punchng.com)
One by one, we got into the river by climbing down a small cliff with the aid of small rope and jumping backwards into our tubes. (ambergrisCaye.com)
This game needs a better climbing down system though there are plenty of areas to just slide down cliffs and sliding from a run works well. (gameindustry.com)