When an organisation is about mother to mother support for mothering through breastfeeding it is hardly surprising that messing with the “mother” bit of that would be upsetting for current members. It is fundamentally changing the focus of that organisation.
As the article says becoming a mother is a significant life change, many of us need support during that time of “matrescence” from those who have been there before. The loss of the word mother further devalues mothers and mothering and makes us invisible.
Parent to parent support for parenting through human milk transfer (includes chest and breastfeeding) has quite a different feel to it...