Agnethe was born in 1947 to mother Agathe Lund and father Villy Wael (1928-98), but she was raised by her grandmother.
[1] At 16, she met her future husband, the blacksmith Aqqaluartaaq Davidsen, whom she married in 1966, and they had two children, Søren (1965) and Heidi (1967).
[1] In 1983, Davidsen was appointed to the Parliament (Landsting) as substitute for Hans Pavia Rosing, representing the social democrat-oriented Forward (Siumut) party.
[1] In 1989, she was elected to the city council of Nuuk, again under the banner of the Forward party, and between 1989 and 1991 held the position of second vice mayor.
[1][3] She was a vocal advocate for hosting the 2002 Arctic Winter Games, which were held in both Nuuk and in Iqaluit, Canada.