Tā juéde nǚrenjia xīnxì, zuò zhè gōngzuò zhèng héshì.
He thinks women are more attentive, so they're well-suited for this job.
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The 家 suffix here is the same one in 孩子家 (children) and 学生家 (students) — it generalizes the noun to a class of people, not a household. Toneless: read as -jia.
usage
Often patronizing in modern usage, especially in 'women shouldn't...' constructions. Common in older novels and dialogue; sounds dated or sexist if used unironically today.