I recall the first time I read a similar thought in one of Roshi Steve Hagen’s books that profoundly shaped my love for the Dharma and affinity with the Zen tradition. Just as birds do not seek the sky, and fish do not seek the water, all of our seeking is in vane.
My seeking behavior (even seeking enlightenment/full awakening) is another form of attachment to something outside of myself. The Buddha taught that I am already complete, and as Shunryu Suzuki Roshi characterized it, I still need a little improvement.