Besides the minhagim involved, there is another hazard in telling people a due date. – nobody’s told the baby! Babies generally arrive when they’re ready. They don’t have a little calendar in which they faithfully count down to the date the doctor gave. And the doctor gives the date based on averages, and each mother is different.
If you give out a specific date, and the baby decides to be “late,” what then? You’ll just have a lot of worried friends and family.
Give the kid (and the mother) a break. Give out only a vague date, and save the worry.