When you greet someone you acknowledge their presence, to not do this is to (western culture) is to deliberatly shut people out, telling them that you do not care about them or take note of their contribution. You should infact be very glad that they keep pointing this out to you, since greetings are generaly only offered to people (northen european culture) to people in your group, and if your parents consider you a part of their group it's a very good possibility they won't kick you out and forget about you when you're 18.
You live in their house, eat their food and ride in their car, you can really afford to show some gratitude.
This is not old fashion, it's current fashion.
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