You don't just blindly reel in anymore. The fish go through fight/rest cycles marked by wiggling. Stop reeling while they fight. If you fish from shore, you can also drag fish onto land using the rod and then pick them up. I also try to limit casts to less than 5m. Finally, use the 'e' key to grab them when they are close to you and out of the water.

Bonus: fishing levels from reeling, not catching. You can level by just max casting on dry land and reeling back in over and over. No fish is required.