Arguing with a jealous friend and still saving the relationship

Hey,

I had another little argument with my good friend. This is my perspective but I am trying to tell it as objectively as possible:

I started noticing she brags a lot and tries to tell how important, wealthy and smart her family is. It is in almost every conversation we have. It bothers me because I don’t know how to respond. I think that people who actually have a lot and know a lot, don’t try to prove it so much. It puts me in an awkward position. She sees herself as a very smart and hardworking woman. However, we are schoolmates and I see how she struggles with any bit more complex task and has trouble concentrating. She failed a lot of stuff but never wanted to confess it. This didn’t bother me and I never wanted to confront her. But now, she started to “wish” (this is how I sense it) I was doing worse and convince me into thinking I don’t know what hard work is etc. She doesn’t want to see the reality and accept some people are doing some things better than her. We had an argument and I am really bad at it. I don’t scream or attack or try to say nasty stuff just to protect myself. I can apologise but she is not like this. She thinks her point is the best, that she has everything sorted out. I don’t know how to find the middle ground. I don’t want to go into primitive mode and just attack or be like her, but by being like I am now (gentle, apologetic and “trying to talk things through nicely”) is making me feel so weak and vulnerable.

How to argue in a productive way to save the friendship? Is it possible to learn to accept and ignore some traits of your friend because talking it out seems impossible?