He had to, though. It wasn't a brave choice, it was best option self defence following the Daily Telegraph's actions. From the BBC article:
"As a result of my parents' addictions my early life was messy, although I had the blessing and gift of a wonderful education, and was cared for deeply by my grandmother, my mother once she was in recovery, and my father (Gavin Welby) as far as he was able."
He added: "I know that I find who I am in Jesus Christ, not in genetics, and my identity in him never changes...
"Although there are elements of sadness, and even tragedy in my father's (Gavin Welby's) case, this is a story of redemption and hope from a place of tumultuous difficulty and near despair in several lives."
"Archbishop Welby, the most senior cleric in the worldwide Anglican communion, says he discovered the real identity of his biological father in recent weeks.
The Daily Telegraph reports that he decided to take a DNA test after it approached him with research it had carried out into his family's background.
"The Bishop of Norwich, Graham James, told BBC Radio 5 live when Archbishop Welby decided to take the DNA test his thought had been to disprove the claim.
"It proved quite the opposite and he discovered this for certain just before Easter and then contacted his mother... his first thoughts were for her rather than anyone else," he said.
"Although she knew the history of her relationship with Sir Anthony at the time, she'd always believed, as had Gavin Welby, that they were Justin's parents." "