I wonder if this was done to be accommodating of same sex couples though? I filled in this form as the "other mother", who didn't birth our child, and I kind of appreciated the phrase at the time. However I'm totally aware that the feelings of the second parent shouldn't trump the importance of using the correct language. It just feels like something that may have been done to be inclusive of kids who have two mums.

Legally, the mother is the woman who gestates and gives birth. Check out this thread on why the word mother is extremely important (has specific status and responsibility in law). Not only for using the correct language as you mentioned, but for the safeguarding of babies, and legal issues esp in exploitative and misogynistic practices such as surrogacy.