Your question made me think of my past experiences as a graphic designer. I would say that the most challenging thing is dealing with clients. As a designer, you will work either as a freelancer doing work for clients or working at a company as a designer doing work based on company needs. Either way, you have to deal with people at all levels of involvement in the process from concept to execution of the final design(s). Some will treat you as a professional, skilled in your craft, and an expert in design, while others with a little know-how of design will think of themselves as designers and will treat you as the hands executing their ideas even if it's your design. Enjoy the easy people (clients, colleagues, or managers) and with patience work to educate the neophyte to the complex processes of design. Hold your ground and be professional always. Best of luck!
Hi Chi. Consistently, one of the biggest challenges in graphic design is dealing with the client. We are often asked to compromise between the client's wishes and our best design solution. My approach to graphic design has always been to see it as problem-solving. The design must accomplish something. It has to convey a message. It has to do work. (The Amazon logo tells you they have everything from A to Z - with a smile.) Understanding that concept and coming up with a clever way to solve the problem is a great way to win over the client. When they understand that there is a reason behind the design and all the elements of it, it makes it harder for them to argue for changes without a purpose.
Whether you freelance, work in an agency or work in a corporate marketing department, there will always be a client with an opinion. As Alwyn said, be patient and professional. It can also be helpful to run your design ideas by other creatives and get their feedback. Doing so, even as a student, can improve your skills by leaps. I wish you the best!