It is actually not a contradiction. Any object (be it an electron or you or a planet) is at once both a wave and a particle. It's just the way G-d set up the universe.
So if you test an electron for wave behavior, it will pass every wave test, perfectly. So an electron must be a wave.
But if you test an electron for particle behavior, it will pass every particle test, perfectly. So an electron must be a particle.
So what is an electron, a wave or a particle? It must be two entirely different things at once. How it shows itself to you just depends on how are are examining it!
It appears the question is how does the electron know what you are measuring for and why does the electron show up for the test exactly how you want to measure it? Why does the electron want to please the tester? Could it somehow be communicating with us?