Some functionality of the dependent packages depend on ImageMagick by definition. This means that the dependent packages (cups etc.) have been built in a way that they require (depend on) ImageMagick to complete certain operations.
So, without a working ImageMagick, cups built by Ubuntu will not work as intended. To make sure all the installed packages work as intended, apt, dpkg and other system tools make sure the packages with unsatisfied dependencies will be deleted from the system.
If you still are certain you don't need ImageMagick on your system, you will have to compile cups and other dependent packages again without linking them against or making them otherwise dependent on ImageMagick. That may or may not be possible using parameters to compilation configuration script (usually invoked by ./configure command). In Ubuntu, maintaining self-built packages is usually not recommended or made particularly easy (you will have to compile the applications again manually to update them, and make sure the applications' dependant packages are compiled again, too).
The practical solutions are using a distribution where self-building applications and handling dependencies across them is meant to be easier for the end-user (Gentoo, Arch, etc.), and alternatively keep using Ubuntu without deleting ImageMagick.