A Direct Line Life Insurance study also found dads are three times more likely to miss out on their child's first words and steps than mums.
Mark Chester is from Who Let The Dads Out?, a programme run by The Bible Reading Fellowship, to help churches support dads and father figures in their local community.
He told Premier nothing should stop dads from being in the delivery room.
"It's just too good an opportunity to miss. Shared experience is like relationship glue really and what a great way to start a relationship and get off on the right foot with a shared experience and being there at the birth of your child," he said.
The study predicted that flexible working and shared maternity/paternity leave would enable both parents to spend more time with their children in the future.
Chester said it was encouraging that most men do want to witness the birth of their children but acknowledged there would be issues such as poor health and work commitments that would stop them.
He however told Premier people should pray for men to value their children's landmark moments.
He added: "I think we should just pray for people that they wouldn't be bound by that fear but actually they would feel some freedom to take a risk - to do something different... find some courage to make some brave decisions about perhaps sacrificing a particular job and taking on a different job.
"Pray for them that they would have clarity in seeing how important this relationship with our children is and how important the early years are and actually it will prove to be far more important than career prospects in the long run.
"Pray for people to be able to see that clearly and just to trust God in the whole situation."
Listen to Mark Chester speaking with Premier's Eno Adeogun:
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