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Luke's failure in the cave was that he went in looking for a fight. Yoda told him that the cave only contained what he brought with him and that he didn't need his weapons but Luke brought them anyway. Because of that failure, Yoda didn't think that Luke was ready for Cloud City. When Luke insisted on going, Yoda urged him to remember his failure in the cave. The screenshot below was Luke's moment of truth. Had he simply retreated after Vader fell backwards off that ledge he theoretically could have reunited with Leia and escaped the city unharmed. But Luke got cocky, was overly aggressive, and wanted to continue the fight. And thus he repeated the exact same failure as before, even to the point of jumping down and entering a corridor very similar in architecture as the one that Vader appeared in on Dagobah. From that point on Luke's defeat was all but assured, as Vader was able to easily turn his impatience and aggression against him.