The bug
When shooting with a bow held in the offhand while in third person it looks like it's pointing towards the ground and there is no hand animation.
The picture on the left is the broken animation in the off-hand. The picture on the right is the animation in the main hand.
How to reproduce
Take a bow
Put it in the offhand slot
Try and shoot with it
Code analysis
Code analysis by @unknown can be found in this comment.
Related issues
is duplicated by
Comments
Confirmed of 15w39b
Confirmed of 15w39c
Confirmed for 15w40a
Confirmed for 15w41b
Confirmed for 15w42a

Affects 15w43a

confirmed for 15w45a

Confirmed for 15w46a by MC-92660

affects 15w47a

confirmed 15w49a

affects 15w49b

shields do the opposite

Finally, someone reported this!! I died many times, when playing on 1.9 snapshot pvp servers, because of it!

Confirmed for 16w06a

confirmed 16w07a

If you could, please add the "bow" and "offhand" labels to this report. I feel like it will make the report more visible

confirmed 16w07b

confirmed for 1.9 pre-1

confirmed for 1.9 pre-2

Confirmed for 1.9

Thankfully, the flood of duplicate bug reports resulting from this bug being in a "stable" major release of Minecraft will knock some sense into the devs & force them to look at the bug that they're all duplicating: this one.

confirmed for 1.9.1-pre1

confirmed for 1.9.1-pre2
Pls fix.

confirmed for 1.9.1-pre3

Confirmed for Minecraft 1.9.1

Confirmed for 1.9.2
Confirmed for 16w14a

Confirmed for 16w15a

Confirmed for 16w15b

Confirmed for 1.9.3-pre1

Confirmed for 1.9.3-pre2
Confirmed for 1.9.3-pre3
Still in 1.9.4
Still in 16w20a
Still in 16w21a

Confirmed in 16w21b
Still in 1.10-pre1
Still in 1.10

Confirmed in 1.10.1

Confirmed for 1.10.2

Confirmed for 16w32a

Confirmed for 16w32b

Confirmed for 16w33a

Confirmed vor 16w35a

Confirmed for 16w36a
16w36a is already listed.

Confirmed for 16w40a

Confirmed for 16w44a
16w44a is already listed.

Confirmed for 1.11-pre1

Maybe add the labels; animation and/or model ?

Confirmed for 1.11

Confirmed for 1.11.1

Either the bug is what's mentioned (no animation), or it's that the bow is usable from the offhand.

Confirmed for 17w06a

Confirmed for 17w13a

Doesn't fixed for now, hope they in another 17w..a

Confirmed for 17w16a, 17w16b, 17w17a, 17w17b, 17w18a, 17w18b, 1.12-pre1, 1.12-pre2 and 1.12-pre3

Confirmed for 1.12-pre4 and 1.12-pre5
Can confirm for MC 1.12.1.

Confirmed for 18w21a.
Confirmed for 15w37a