Do you have administrator privileges on the computer that you're trying to install Tomcat on? Normally, the Windows installer installs Tomcat as a system service. Maybe you don't have rights to install system services on your computer.
You can also use Tomcat without installing it as a service. The easiest way is to download the ZIP version instead of the Windows installer version. All you'll need to do is unzip the ZIP file in a directory and run the bin\catalina.bat file to run Tomcat.