Since chemistry is generally defined as a difficult major reserved for only the brightest and most studious students, a girl who is "no chemistry major" is likely of average or below average intelligence.
This phrase is most often used to refer to women who perceive themselves to be much smarter than they actually are.
Jimbo: Did you hear Karen trying to argue about the economy last night? She really made herself look like an idiot.
Nelson: Yeah, she's no chemistry major.
Fogey/fogy /fougi/ sl. (early 18C+, orig. Scot) old-fashioned, stuck-in-the mud.
Person with old fashioned ideas which he is unwilling to change: Come to the disco and stop being such an old fogey!
You think me an old fogeyand an old tory, his thoughtful voice said. I saw three generations since O’Connel’s time. I remember the famine. Do you know that the orange lodges agitated for repeal of the union twenty years before O’Connel did or before the prelates of your communion denounced him as a demagogue? You fenians forget some things. (James Joyce, Ulysses. Penguin Books,1992. p. 38)