Why a "positive" often is not
The arithmetic that nobody explains at the appointment.
A test can be extremely accurate and still give you a positive result that is usually wrong. This is not a flaw in the test. It is arithmetic, and it depends on how common the condition is.
Imagine a test that catches 99% of cases and has a false-positive rate of 0.1%. If the condition affects 1 pregnancy in 10,000, then in 100,000 pregnancies the test flags about 10 real cases and about 100 healthy pregnancies. Ten out of one hundred and ten positives are real. The other 91% are false alarms, from a test that is 99% accurate.
The number that answers "how likely is this to be real" is called the positive predictive value. It is the number you want, and it is almost never the number you are given.