Hey! So the whole sentence means something along the lines of "the reason for the continued increase of educational expenses in household expenditure even amidst an economic depression, can be seen as the passion for education that parents have, which leads to them trying not to cut down on educational expenses for their children, even if it means not eating and not spending (on other 'things')." So the '안 먹고 안 쓰더라도' part roughly translates to "even if they don't eat and spend (money on other things)" and the '으려는' part is something like "trying to" so in this case, it means "trying not to cut down on (educational expenses)". I'm sorry if this isn't clear, but feel free to ask if you don't understand!

I would say this is just a simply not that good writing. You can easily notice that they used '에서' twice at the beginning of the sentence and that sounds really clumsy to me. I would rephrase that like "경제 불황이 지속되는 가운데 가계지출에서". And 않으려는 is a short form of 않으려고 하는. 하다 = To do 하려하다 = To want to / To try to / ... 않으려고 하다 = Not to want to / ... I will just write down the full version of the paragraph under my understanding. 경제 불황이 지속되는 가운데, 가계 지출에서 교육비의 비중이 계속 높아지는 '것은'[=이유는] (부모들이 값비싼 음식을 자주) 안 먹고 (지출이 높은 경제활동에 생활비를) '안 쓰더라도'[=안 쓰는것을 감수하더라도] '자녀 교육비는 되도록 줄이지 않으려는'[=자녀 교육비에 들어가는 돈 만큼은 되도록 줄이고 싶어하지 않는] (부모들의) 교육열 때문인 것으로 해석해 볼 수 있다.