I faced this my senior year of college too. What drove me out of the rough was Dweck's Mindset. Get your hands on a copy if you haven't read it yet. The take-away for me was that the apathy I sometimes felt was a kind of scapegoat for avoiding situations where I could fail. Instead of increasing my effort when I was faced with the hardest problems, I decreased it by avoiding them. This reduces the probability of failure but also ironically of success as well, which tends to sting in the long run if you don't catch it.
You've got a point apathy being a mechanism to avoid, or even rationalize failure.
I realized something else: that winning gives you ownership and confidence.
To use my previous example, If I had diregarded "interest" in algorithms and gotten stellar grades in algorithms classes just for the sake of "winning", I would come to be proud of how good I am at algorithms. I would become empowered, I would like the feeling, and I would like algorithms.
