You let go, it shoots back up.

In the game's code the fish isn't random: it chases a target you never see. Every frame it speeds toward it, and its difficulty number decides how often that target moves and how far. A Carp (difficulty 15) picks a new one about every 4.4 seconds; the Legend (110) more than 1.6 times a second, anywhere in the water. Even the first target is the difficulty as a height: 15% of the way up for a Carp, over the top for the Legend. Smooth, dart, sinker and floater fish are small edits of the same rule. The fish's rule reads the same in the code of late 2016 (v1.11) and of today's 1.6.

In 2013 Eric Barone (ConcernedApe) wrote that he wanted a fishing minigame "that requires a little bit of skill". Two weeks after launch, PC Gamer asked him about the outcry over fishing. His answer: "it's one of the things I'm most proud of in the entire game, so I'm not going to change it." In 1.4 (2019) he did add a training rod for beginners and made the bar's bottom edge slightly more generous.

The lake, the lantern, the fish and the angler are our own pixel art, and every fight on screen is our own simplified version: a port of the game's rule with the game's numbers and our own dice (the first fight is a difficulty-75 fish, the Catfish's numbers, at fishing level 6). Not affiliated with or endorsed by ConcernedApe.

Which fish took you the most tries?

Sources: ConcernedApe, "Dev Update", 5 Sep 2013; Tom Marks, "Interview: What's next for Stardew Valley", PC Gamer, 10 Mar 2016; the official Stardew Valley FAQ; the game's code (BobberBar, read in v1.11 and 1.6 decompiles); the Stardew Valley Wiki's fish table.
Sounds: our own, made in code.