But along with many other attitudes, that's beginning to change. Giving a new twist to family ties, more banks are assuring donor and offspring do meet many years later, reports CBS News Correspondent John Blackstone.
One American family, Mary, Christina and Phillip, are writing new rules. Mary and Christina are mother and daughter. Phillip is the man who made that possible.
"I was reading the newspaper and it said, 'Help loving families have children,'" says Phillip.
Phillip donated to a sperm bank almost 20 years ago.
"He cracked me up," says Christina. "He's just like me only in guy form."
Christina has long known she was conceived through artificial insemination, but meeting Phillip face to face -- an event recorded in a friend's photographs -- is unprecedented.
Phillip and Christina are the first donor and child to meet through a program of extraordinary openness at the Sperm Bank of California, a program breaking an unwritten rule of artificial insemination.
"For decades, families were counseled by everyone to lie: 'You should not tell your child this is how they were conceived,'" says Alice Ruby, of the Sperm Bank of California.
In vats of liquid nitrogen at the Sperm Bank of California, only numbers identify the frozen samples. But most donors here make an unusual agreement: to eventually be identified by any children who are their offspring.
When Christina turned 18, she was able to get Phillip's name and left him an unusual phone message: "I'm kinda like your donor, daughter, sperm thing."
"I didn't know how to put it – it was kinda weird," she says.
"I just wanted to find out later to see how this person turned out, and for me it would be only fair for them to know who I am," says Phillip.
Twenty years ago, Mary, already the mother of two, badly wanted to get pregnant.
"I was getting older and mine were growing up, and I just wanted another baby," says Mary.
She knew little more than that the donor was African-American.
"My ex-husband was an African American so I already had African-American children, and I wanted her to match," says Mary.
In meeting Phillip, Christina says she's not looking for a father, just looking for some answers.
Some worry that lifting the secrecy could present psychological risks for the children of artificial insemination. But Christina says she's been rewarded by a better understanding of that part of her she can learn about only from Phillip.