In the USA, there is a taboo around discussing money. Finances are regarded as being more personal than health. People will rather talk about the results of their last physical than about their bank accounts.
There is also the fact that “making it on your own” is considered a virtue, so admitting to growing up with a proverbial silver spoon seems like admitting to a deficiency in that virtue.
Furthermore, for many teens from affluent families whose social circle includes people who grew up with less money, there is also a sense of embarrassment at having an easier life than their friends and peers. For wealthy kids whose social circle is mostly kids with less money, being more affluent may also seem like something which makes them being different tan the rest, which is also not something that any person likes having, especially at that age.
There is also the very real and justified feeling that speaking of one’s wealth can be construed as bragging. In the USA (and elsewhere), bragging about oneself is considered rude, even about genuinely remarkable achievements, while bragging about stuff which a person did nothing to achieve is far worse. I think that many full pay students feel that advertising their full pay status would seem like bragging.