横分け is a word that refers to "side-parted hair style", not the type of the glasses he wears. 横分け of men's hair is better known as 七三分け【しちさんわけ】 (literally "7:3 parted").
The combination of 横分け and 眼鏡 is a stereotype of typical middle-aged Japanese businessmen like this:
横分け is usually not used as a derogatory term, but some Japanese people find 横分け as being mediocre or a bit old-fashioned. (And there are also people who find 横分け眼鏡 cool).
Anyway, she seems to dislike 横分け眼鏡. Maybe she thinks it looks too old for his age.