Not sure if you're still pondering over this topic.
Personally, I feel that you should get your own student credit card, because:
It helps you build credit score. By owning a student credit card, you are the primary cardholder of the credit account. This means that CBS (and other financial institutions) now have a way to determine how well you manage your credit. Having a good credit score can be beneficial if you are planning to take out a loan in the near future, for buying a house or a car. As a supplementary cardholder under your parents, no credit account is opened under your name - instead your parents have 2 credit accounts open. This basically means that using it will not build your own credit score, but instead, your parents'.
It gives you a chance to cultivate good credit habits at a young age. You can figure out things like how to make credit card payments online and get used to paying off your bill punctually every month. This will set you up for success and confidence when you eventually own your 1st proper credit card after you graduate.
As Nicholas has mentioned, student credit cards offer dismal rewards. That's why earning rewards shouldn't be the main goal of using a student credit card, but rather the above points I mentioned.
If you want to focus on rewards, it might interest you that students are able to apply for secured credit cards, which are "adult" credit cards with high rewards rates, but require you to have a FD with the bank.
If you're interested to find out more, check out this post https://www.thefrugalstudent.com/credit-cards-for-students-how-to-get-them-why/.
Hope this helps!
Student credit cards often have inferior features and benefits as compared to normal credit cards. You could benefit from having different cards from different banks in order to take advantage of bank promotions. Some banks offer sign-up bonuses too for students from time to time, so do keep a lookout!
If privacy matters to you, you should know that all transactions by the supplementary cardholder can be seen by the main cardholder.
Instead, you can help your parents look through household expenses and optimize their spending! For example, if they are chasing miles, it would be good to separate spending by categories and spend on different cards, such as 4mpd on online purchases using Citi Rewards. The Milelion is a good place to start if you want to find out more.
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