In my opinion, the answer is banal and obvious. Because on the day of conception, the sperm only fertilizes the egg and conception occurs. Few people know, by the way, on what day it happened.
A birthday is the day when you were born and crawled out of the womb, when you separated from your mother and became a human being
And the child is not just sitting in the womb for 9 months. At first it's not a child at all. This is a zygote, an embryo, an embryo, a fetus closer to the middle of the pregnancy. It grows and develops and is legally not considered a person as long as it is completely dependent on the mother's organism
If you meant why the child's age is not considered from the day of conception, but from the day of birth, then the answer is almost the same ... Because it is impossible to know what day you were conceived. If the date of birth, that is, the recognition of the child as a person, was legally from the very moment of conception, then this would bring a lot of problems. Firstly, not every pregnancy ends in childbirth. Or because the child is unwanted, or the fetus is sick, or the mother is in danger. Or simply the egg fertilized but came out with menstruation. And if we consider the day of conception as a day of birth, that is, give the status of a person, then it is necessary to track each birth of life and mortality (which will be catastrophically high). And how do you imagine to control this?
In some places on Earth, a person's age is considered from the day of conception. I remembered such a footnote in the collection of fairy tales of the peoples of the world. The footnote refers to a Chinese fairy tale.
Because the date of birth is the date when the process of birth took place, not conception. The date when the process of conception took place will be called the date of conception, not birth. But few people know it and it is not always possible to calculate it even for parents.
Stupid question for me. The date of birth is so called because it is the date of birth. Besides, who cares when the child's parents were engaged in conception? Think about it yourself.