Because acknowledging age and generation is treated as a basic form of gratitude. Greeting the oldest person in the room first — by title, individually — recognizes what they have carried, and doing it in front of everyone makes the recognition public.
In many households children are taught to khoanh tay (fold arms across the chest), slightly bow, and greet each adult by name and title: "Con chào bác," "Con chào cô Hương." At a large gathering this can mean circling the entire room before you're allowed to disappear with your cousins.
The order matters. Oldest generation first, then down. Within a generation, older before younger. Guests are usually greeted before family.
What makes this feel intense for kids raised outside Vietnam is that it is public and evaluated. Adults notice. Parents notice whether you noticed. A child who forgets is often described not as shy but as không biết chào — doesn't know how to greet — which is heard as a comment on the parents.
The upside is that it is one of the easiest things to get right as an adult, including for people marrying into a Vietnamese family. Learn three or four titles, greet the elders first, and you will be treated as someone who understands.
Formality varies enormously — some families are strict, some are relaxed, and expectations often soften across generations and abroad.