The bug

Since 1.8 punching animation get completely cancelled when using an item such as blocking, eating, aiming in first person. This does not happen when punching while using an item that plays the "take" animation (punching while switching or throwing - before 1.14). It is inconsistent with the third person behavior as the punching animation isn't cancelled (-except for the bow before 1.16). 

How to reproduce

1. Launch any version before 1.7
2. Punch and eat/block at the same time
3. Do it in third person
   →  The punching animation isn't cancelled in both first person and third person
4. Launch any version after 1.8 (if possible 1.16)
5. Punch and eat/block/aim (note: only 1.16+)
6. Do it in third person
   →  The punching animation is completely cancelled in first person but not in third person

How to fix

Either make swinging animation get cancelled in third person (but this will be inconsistent with the "take"+punch animation) or make swinging animation no longer get cancelled in first person (this may be a more adequate solution, as people already use animation mods in 1.8).

Note: This may be an intended feature in Java Edition 1.8, as animations got revamped and using while breaking is no longer possible (you can no longer place a block while breaking another one).