Why does the miller ask Beetle if she has gone daft?

Jane, the wicked midwife, is shouting at poor Beetle again. Having lost another one of her few remaining teeth and having also broken her ankle, the old crone is in a foul mood, and she throws copper pots and cooking spoons about the cottage. She takes out her growing anger on poor Beetle—except for the fact that she is no longer called Beetle, says Beetle; her name is now Alyce. On hearing this, Jane splutters with contempt. The very idea of a young waif found on a dung-heap having such a delightful name is simply way too ridiculous for words. As the nasty old midwife continues throwing pots at her, Alyce figures it is best to go outside.
Outside, in the summer morning, Alyce comes across the cat that she likes to pat and stroke. Now that she has finally plucked up the courage to say her new name out loud, Alyce wants everyone and everything to hear about it, even the cat. As the cat playfully rubs up against her, Alyce tells the cat that she wants to know what her name is. Alyce then goes through a list of common cat names, hoping that the cat will respond to one of them. A passing miller walks by and hears Alyce talking to the cat. That is why he thinks she may have gone "daft" or, in other words, a little mad.