I read about other benefits to turning into torpedoes; if you turn away, you may oversteer while dodging torpedoes that are chasing you from behind and you may fail to dodge IJN CV torpedoes that converge. But I ask only about the question in the title.
The other reason is that if you turn out, your odds of taking more torpedoes than you would if you turned in are pretty high.
Let's take this situation. For a torpedo to hit you, it needs to occupy the same X and Y-coordinates as you[r] ship.
Staying broadside means that you maximise your length along the Y-axis, so many torpedoes can hit you at once. You want to dodge left or right to minimise your profile along the Y-axis, decreasing the chance that a torpedo will intersect you along that axis.
If you steer away from the torpedoes, you move into the same X-direction as the torpedoes. This means that you spend a very long time on the same X coordinates as the torps, and therefore there is a very long time in which the torpedoes can hit you. In the worst case scenario, you can get hit by every single torpedo in a salvo by catching them one after the other, because you spend so much time on the same height as the torpedoes.
If you steer into the torpedoes, you minimise the time in which you occupy the same X-coordinates as the torps, therefore there is only a very short time at which they can hit you.
I still can't grok why turning into torpedoes is necessarily safer. See the pictures modified by me, in ian9167's comment beneath.
If I turn left but choose 'Stop' as my speed, wouldn't only #1 hit? I might've slowed enough that #2 (diverging as time passes) will pass ahead.
If I turn right, I must pick 'Full' as my speed (or else my ship will sit broadside and be torpedoed by 1 and 2). But then wouldn't both 1 and 2 hit me?
As you turn away, you increase the distance to the enemy torps, while still travelling into the "danger zone". Thus giving them more time to travel and hit you as shown by my next level paint illustration. Go right and get hit by 2. Go left get hit by 3.
Equally however you can outrun slow torps by slightly turning out of them - it depends on the situation! But pretty much always turn into carrier torps.