Neither do they want to do better than boys

楼上的说法可能不太对。。。

they are afraid to appear less feminine and so, less attractive
她们顾虑会显得比较缺乏女性味，从而比较不吸引人。关键是跟谁比呢？那些不去跟男孩比高下的女孩。完整的句子应该是：
they are afraid to appear less feminine (than those who do not want to do better than boys) and so, less attractive (than those who do not want to do better than boys)
这样当然很冗长，重复。你看到的句子简略得多，但意思是一样的。

paraphrase 仅供参考：

They do not want to do better than boys too, because they want to remain feminine and so, attractive.

这句话显然是对一个女生说的，句子的意思，就是说千万别在男孩子面前太逞能，因为如果那样的话在女孩子的光环下，自己会悍然失色，很没面子。

那个句子省略了than，原句是to appear less capable than feminine and so, less attractive.
这个你记住就好了没必要去理解，老外的习惯用法，有历史的。