The main role of a cruiser, as far as battle is concerned, is kill destroyers. Yes, contesting and supporting is also a part of your job but fighting is a large part of that.
In order for a cruiser to kill a destroyer easily he must have no distractions i.e. other ships. You should not be engaging in battle with other battleships or cruisers if you can help it. Killing a destroyer is your first contact priority.
It is the main job of a cruiser to kill destroyers so that destroyers can do their job.
It is the battleships main job to kill cruisers so that you can do your job.
Destroyers cannot do their job until you do yours.
If destroyers are not an available target, dead or none in game, then other cruisers will be next in line, then battleships.