<p>Since your parents seem to be sensitive to what others think/say, indicate that CC is not for stupid people, but rather for people who don’t have money - students whose parents have money go to 4-year schools and stay in the dorms ( when available, if the parents really have money, parents pay for the nicer dorms.) In tha tmindset, private is better than public. And living on campus v. commuting is always seen as “due to lack of funds”. So if your parents are concerned about looking poor, this may “work” to sway them a little.
Tell them also that only students with serious problems do purely online college, ie., in the US it conveys either that the student has serious behavioral issues and can’t be left in the company of his/her peers (drugs, mental health, aggression -look at some reactions on the other thread, asking about your problems/mental state: when parents won’t let kids go to sleep away college the assumption is basically they can’t afford it or the kid has a mental problem) or that the student and his/her parents know nothing about education because purely online undergraduate degrees without a brick and mortar university + on campus classes are neither well-recognized nor equivalent to “real” classes. In fact, these universities often prey upon first generation students, families where people have little education and can’t recognize the problem, etc.
If your parents are status conscious they may not want to appear to Americans as being poor, uneducated, or saddled with a “mental health afflicted” daughter. 
Since you can’t mention CC, you could say it’s what your classmates, teachers, ang guidance counselor all immediately thought about and that felt bad for them but apparently that’s how Americans think.
Just saying this as points you may be able to use.
Oh, this is about for profit schools:
<a href=“http://www.sfgate.com/education/article/California-sues-3-for-profit-colleges-4885409.php[/url]”>http://www.sfgate.com/education/article/California-sues-3-for-profit-colleges-4885409.php</a></p>