It can be a little frustrating to lose a fish especially when you were so close to catching it. However, fishing in the game increases with difficulty when you use certain lures or when you happen to get a rare fish species to latch on. The rarer the fish, the harder it is to catch it, as they tend to wiggle around and cut loose from the lures.
When you have the fish closed in to the green circle, make sure not to lift your finger from the screen until it jumps out of the water.
Good luck!