Left over from MC-127094.
This is inconsistent - all cases of players dropping items should appear equivalent.
NOTE: This has not actually been fixed in 19w42a, and is still present in subsequent versions.
To reproduce:
Open the survival inventory in either creative or survival mode.
Hover over an item in the inventory and press the drop key. - Notice how your character's arm doesn't animate as if they had dropped an item like in the non-inventory case (although the hand may move up and down if the dropped item slot is the selected slot).
Drag an item out of the inventory screen, and release it, dropping it. - The character doesn't display an animation for this case either.
Now fill your inventory with items, switch to survival and have a stack of honey bottles ready. Drink one of said honey bottles and note how the dropped honey bottle does not cause your hand to swing as if you had thrown said item put after consumption. While there are other behaviours that cause such item dropping, such as filling bottles and buckets with a full inventory, a hand animation already plays for the action and so none is needed for this.
Related issues
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Relates to MC-160981

Confirmed in 19w38b.

Confirmed in 19w41a

Can still reproduce in 19w42a - from using the B key to drop items, as well as dragging them out of the inventory and releasing them.

Please reopen.

Is this even a bug? You don't do anything with the item you're holding, so why should the hand that holds an item move forwards?

Because that's obviously the case with dropping from the hotbar.

Still affecting 19w44a for both cases, please reopen

I can confirm that the behaviour of this report happens in 19w44a, but I do not agree that it is a bug.

Still affecting 19w45a

Still affecting 19w46a, I do not know why this still hasn't been reopened yet.

Still affecting 19w46b

Relates to MC-96782 where it states the following which may help fixing this:
The method public EntityItem dropPlayerItemWithRandomChoice(ItemStack itemStackIn, boolean p_71019_2_)
of the class net.minecraft.entity.player.EntityPlayer
is used to drop items while having a container GUI open or when you get an item but have no space in your inventory.
This happens under multiple circumstances, for example when you press "Q" (or the key you assigned) while having a container GUI open or when you close your inventory while you have items placed in the crafting grid. This is report is about the latter one. In 1.8 all cases except player is pressing "Q" are handled as item was not dropped by player, but in my opinion that is not correct.

Affects 1.15-pre4.
I may add this suggestion as well if fixing: No matter which item you hold in, the hand animation should show when throwing away anything from the player. For example, if you hold a stone block and throw away an apple from the inventory it should maybe show the animation. The reason for this is just that it seems logical.
See
[media]
That's kinda the point of the ticket

If you drop an item by closing a UI, it currently also doesn't play the hand animation. MC-194699