Why did the frog call her 'a brainless child'
Because she could not think for herself and let the frog make her decisions for herself. It's also the frog way of showing his superiority (that in a way he was always her teacher and therefore above her) in a passive way, as it sounds like he's talking about a naughty child making mischief .
In Vikram Seth's poem "The Frog and the Nightingale", the frog calls the Nightingale 'a brainless child' because the nightingale was so innocent and naive that she couldn't make her own decisions or be independent. She should have avoided the frog from the start itself. The Nightingale couldn't figure out that the frog was overstressing her and she was so scared to approach him and tell her problems. Moreover, she surrendered herself to the frog which gave him the opportunity to torture her till her end.