When you box, should you punch with your elbows pointing down, or to the side?

When you box, should you punch with your elbows moving down, or out to the side?

I asked this same question (more or less) at the boxing gym tonight. It seemed easier to rotate the elbow outwards and upwards to turn my fist on jab type punches.

But the trainers said that leaves you open on the side, you should keep your arm straight and go straight forward during the punch.

So now I have to make the extra effort to turn my fist to horizontal in the process of doing the jab.

You do both ,but at different times.
Each has its advantages to suit the different distances and targets and heights of your opponents .

You have to consider the added risk to your little finger when throwing some finishing shots to the harder boney targets with elbow down vertical fist landing the middle knuckles as opposed to the elbow out landing horizontal fist landing the top two knuckles.

Eg, Throwing a close in hooks to someones temple who is taller than you would be risky to your pinky knuckle ..elbow down; but not so on a shorter person or someone whos gone low trying to avoid .
If you were to throw the same thing (vertical fist elbow down) low as kidney hook it would allow you to turn in a little more and use your leg ,hip easier and get your weight behind it better.

Regarding straight shots,
specially if the opponent is shorter and you have a longer reach:(and even better if your in opposite stances) You can throw your jab over the top of his from the outside,on an angle and block his jab while landing yours .

That doesnt work with your elbow out, it only works elbow down and with a vertical fist.

I think at first dont confuse the issue ,get down what works for you easier ,master it, then bring in the other, but only when the times right and the target is right.

Practice all of them shots on the bags, but do it with the main reason why and the target set in your mind !
so then you can experiment with the added weight behind the shots or the body/footwork release to get you passing through a situation into a better position as you do them shots etc.