I think everybody needs to go read the lyrics to my name's WOMEN.
Ayu specifically states that she still enjoys 'pretty things'. But, she feels the need to defend this as men believe that this image is a reflection of a personality. When it isn't.
Basically, she's saying that women should own this. This is OUR thing. We shouldn't have to abandon it to gain respect. If we want to look pretty or cute, we can. It shouldn't have that submissive or innocent label attached to it because it is simply not true.
This is where Chibi-Chan is also correct. Ayu basically addresses this issue in the song; women ARE shown as being light-headed, immature, and childish, and this in turn, is how men see them (in her opinion; of course not everyone is like this). And it is wrong. Ayu just thinks that we shouldn't have to give up the image that has created this illusion...