I was reading on the creation of matter shorty after the Big Bang, and about the fact that more matter was created than antimatter. Then there was this explanation that kaons and antikaons don't decay into the same particles, and how this could explain the asymmetry between matter and antimatter. Is there any modern explanation why this kaon asymmetry occurs? I'm a layman so I'd prefer a non-technical explanation.

The singularity in which our cosmos begins can have two sides. Since time begins in that singularity

it can have a negative axis. Along the negative side of the axis the time will grow in the negative direction.

Negative time in this sense does not mean it goes backwards. It will be the time just like time is measured

on our side of the singularity. Please try to imagine two cones glued one to the other by their point.

I was reading on the creation of matter shorty after the Big Bang, and about the fact that more matter was created than antimatter. Then there was this explanation that kaons and antikaons don't decay into the same particles, and how this could explain the asymmetry between matter and antimatter. Is there any modern explanation why this kaon asymmetry occurs? I'm a layman so I'd prefer a non-technical explanation.

"Why" is a very difficult question to answer. Modern theory explains how and what, but I believe why is unanswered.