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This is mostly because Holden cannot handle emotion himself. His fear of relationships and delusions of self-authenticity drives him to reject the emotions of others as phony or insincere.
Holden thinks that the woman who cried through the movie was a phony because she was with her child who needed tending, and the woman ignored the needs of the child. Throughout the movie, the child complained about needing to use the bathroom, and the woman would not be bothered to take the child, admonishing the child to wait. I think Holden felt as though this woman couldn't possibly be a person who felt deeply, considering she was blatantly ignoring her child's needs and putting her own first. Holden found her behavior shallow and uncaring, which made the fact that she was crying throughout the movie a phony thing to do.