Asking after the household, and what that greeting carries
Some greetings reach past the person in front of you to the people they belong to, and the reach is the point.
In many households and many settings, the standard greeting is not addressed only to the individual. It asks after the family, the household, the health of an elder, the children, the people at home. To ask only about the person standing there would seem oddly narrow, as if you had noticed the branch and ignored the tree. The greeting locates somebody in the web of people they belong to, and doing so is the compliment. Answering it is straightforward, because the reply is usually as formulaic as the question and nobody expects a genuine household report.
Elsewhere the same enquiry can feel like an intrusion. Where the default assumption is that a person appears in public as an individual, questions about family read as personal rather than polite, and can imply an intimacy that has not been established or an interest in circumstances somebody would rather not discuss. The person asking meant the warmest thing available to them. The person receiving heard a door being opened onto private ground. Both readings are entirely reasonable and neither party has done anything wrong.
This is the honest, uncomfortable centre of the whole subject: a greeting that is warm in one place is intrusive in another, and there is no universal setting. What travels well is attentiveness. If an enquiry after your household arrives, it is almost certainly generous, and can be received as generosity even if you answer only in general terms. If your own warm enquiry is met with a short answer and a change of subject, that is not coldness. It is a different map of what belongs in the opening moments.