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Gura meant everything she said about streaming and was prepared to spend time with you. Her family then appeared and wanted to spend time with her instead.
You will never be more important than a person's family. You are objectively less important than Gura's family and always will be. You can cry and moan but "Prior engagement" lawyering means nothing. You can complain about it being rude, it means nothing. You are nothing in comparison to a person's family.
Tough fucking shit. You aren't even her friend, you will NEVER be on the same level of importance as her family.