I think it is because text is usually read left to right and is left aligned. You generally don't read your own messages, so makes makes more sense for them to be on the right (albiet left aligned on the right side, usually). For languages that are right to left, I would imagine it may be reversed.
Discussion
Makes totally sense to me, this way it feels just more naturally.
This.
But your bubbles are often more highlighted than others and this may seem strange. I can only explain it as a way to easily trace back to a point in the conversation by following your messages upwards, which are easier to remember; this is especially useful in a multi-user chat where the ratio of your messages to the total is particularly low.
Yeah, it does seem that there is more contrast for your own messages (text, text background to chat background). Often chat messages from other people will match the display dark/light settings, while your own will be reversed. It doesn't seem all that consistent though.