(sorry, duplicate or MC-92330)

Fishing does not increase the statistics in the menu.
All objectives based on fishing (stat.fishCaugh, stat.treasureFished and stat.junkFished) don't work too.

Easy steps to verify:
/scoreboard objectives add fish stat.fishCaught
/scoreboard objectives setdisplay sidebar fish
/scoreboard players add @p fish 0
/give @p minecraft:fishing_rod
/enchant @p minecraft:lure 3
And try fishing.

Edit, found the original bug post too late:
https://bugs.mojang.com/browse/MC-92330