When one thinks of the axes for two-dimensional space, one envisions two axes that are perpendicular to each other. The $x$ axis increases horizontally from left to right, and the $y$ axis is vertical and increases from down to up. This has the advantage of being a convention which is usually followed, although in some software such as game-making software, I noticed that the $y$ axis increases from top to bottom.
When I learned about the three-demensional space axes, I assumed intuitively that the $z$ axis would be a natural extension of the axes of two-dimensional space -- that is, the $z$ axis would be perpendicular to the $x$ and $y$ axes -- horizontal, increasing from where it is close to you to where it goes far away from you. However, I learned that that wasn't the case. The axes seem to be orientated much differently.
Where did the currently accepted convention originate from, and why isn't it more similar to the two-dimensional space axes?