Astrologers asking a client for a birth time are not being fussy. Several components of a chart change substantially within minutes, and without a time those components cannot be placed.
Time determines the rising sign
The rising sign is the zodiacal degree on the eastern horizon at the moment of birth. Because the earth rotates, that degree advances continuously through the day.
A full zodiac passes the horizon in roughly twenty-four hours, so the rising sign changes every couple of hours. Two births hours apart on the same day carry different rising signs.
In most systems the rising sign anchors the entire house structure. Getting it wrong displaces everything built on it.
House placement depends on that anchor
Houses divide the chart into sectors associated with areas of life such as work, home, partnership and health. Their boundaries are calculated from the horizon and the local meridian.
Without a time, planets can be placed by sign but not by house. The interpretive layer concerning which area of life is involved becomes unavailable.
The moon compounds the problem, moving quickly enough that its sign can change during a single day. A birth near that boundary is genuinely ambiguous without a time.
American records vary in what they contain
Birth certificates in the United States are issued by states, and whether a time appears depends on the jurisdiction and the era. Some record it routinely and others omit it entirely.
Long-form certificates more often carry a time than the short versions issued for identification. Ordering the long form is standard advice among astrologers.
Hospital records, baby books and family memory serve as fallbacks. Each carries its own reliability problems, particularly rounding to convenient hours.
Practitioners have techniques for missing times
Rectification attempts to estimate a birth time by working backward from known life events and testing which time best matches. It is laborious and its results are contested within the field.
Some astrologers instead cast a chart for a fixed reference time, typically noon or sunrise, and confine interpretation to what does not depend on the hour. The limits are stated openly.
Others decline to work without a time at all. The disagreement is about how much can honestly be said from partial data.
Daylight saving and time zones add practical errors
American daylight saving rules have changed repeatedly, and adoption varied by state and even by locality in some periods. A recorded clock time may not correspond to the standard time assumed.
Time zone boundaries have also shifted, so a birthplace may have observed a different zone than it does now. Historical tables exist precisely to resolve this.
Software handles most cases automatically but relies on correct place and date entry. A mistyped town can move a chart by an hour without any warning.