..and it's a lot harder than just shooting another satellite up to bring the old one down. you have to match not only the speed of the target satellite, but the altitude and orbit it's in too.
once you've done that, you can't just attach to it, fire off thrusters and deorbit it; Newton's law still applies. You'll bump into it and according to the 3rd law the target will apply an equal and opposite force. you can't shoot it with a harpoon cause that'll cause more debris.
but let's say you do attach to it somehow or utilize something like electrodynamic tethers (which is what the Japanese Space Agency, JAXA) is using. you can't just throw it back to earth and hope the atmosphere does the rest; you have components that may not completely break up and may rain down upon populated areas(c1).
usually once a target satellite is acquired, it is moved to a graveyard orbit away from operational satellites.
i was going to submit an application to YC to startup a space company dedicated to space debris mitigation but it seemed a bit too complex.
(c1)-This is why most of our spaceflight launch locations (Cape Canaveral, Vandenburg, Wallops) are on the coasts; they fire away from CONUS so just in case there is a catastrophic failure, the debris doesnt rain down on your house.