Mac shifts desktops on maximizing
You're simply confused as how to operate the system properly. When you think you're "maximizing" the window, you're really full-screening the application.

In order to "maximize" the window, you'll need to hold down the Alt-key while clicking the green "+" button in the top left corner of the Chrome window.

You can also maximize windows through other means - such as through an application such as SizeUp! or similar.