Break Fishing Rod

You can find Fishing Rods premade as loot. They are a 41.7% chance from Small Ocean Ruins Chests (in a large ruin, these are the chests in the outside sections) and 21.7% chance from Large Ruin Chests. If you whiff on chests, there is a small chance (3.5%) that Drowned spawn with a fishing rod, and an 8.5% chance they will drop it if killed. 

In the new Abandoned Camps, fishing rods are a 33.3% chance from Barrels, and 27.5% chance from non-copper chests. You can use the cushion in that structue to break it (see below).

A fishing rod has 64 durability and loses different amounts of durability in different ways.

• Hooking a solid block costs 2 durability

• Hooking an item costs 3 duability

• Hooking a non-item entity costs 5 durability

1. If you are near an animal, go up to it and spam right click. Cows, Sheep and Pigs are generally better than Chickens if you have a choice.
   
   

2. If not, you can still easily craft and hook a boat. It helps to minimise hooking distance to place the boat a block up so it's at head height. If you are doing a Jungle Temple route, you need 3 logs going in to do this.
   
   

3. If you have an Abandoned Camp, you can hook a cushion if it is there already.
   
   

4. If you are on a Desert Temple seed you can hook primed TNT, though of course being able to do this without blowing yourself up is an aspect of skill. If there are no clear mobs around, you can break a fishing rod this way, by overlapping TNT with hooking, and the more TNT you use, the safer this method is.
   
   

5. Lastly, a woodless and mobless setup involves throwing all your  except the rod on the floor and hooking them towards you (this is slower than any other method but can be faster than e.g. leaving a jungle temple to punch more wood for a boat). It's helpful to have hitboxes on for this method.

You can also see this resources post that also mentions some ways to do this goal.