Actually, I think that one at least has some history to it.

The disk drive was one of the first ways to store information between computer sessions as the first computers didn't have built in storage. You would create a program, run it, and then when you shut the computer off it was gone. Since the disk drive was used to store programs for later, or "save" them, the icon was born from the physical object.

Sharing, conversely, doesn't really have a real world example to base the icon on. Maybe two hands exchanging things? Perhaps two arrows to illustrate the ability for things to go both ways? Maybe a set of interconnected dots to show the connection between things? Any of them could work, so the iconography is less clear.

The iOS one looks like the standard "exit" symbol you see in airports around the world. It doesn't suggest sharing anything to me.

As an Android user why does an arrow out of a square signify sharing something?

It’s sending something outside of your device (the box).

Oh ok now I picture the ios one. I've grown up with both. I do prefer the android one more though. But I also dislike ios design elements.

I see the Apple one as just showing that a menu will come up, it's just visually showing what will happen when it's pressed, and that happens to be the share menu.