Sometimes people become so hopeless that they sink into depression or commit acts of violence. when this happens, human services professionals and others may stage an intervention. this is a forced interference in the person’s life. why is this an acceptable step to take?

The step would be acceptable because a person who is severely depressed cannot physically realize that life goes on. The chemicals in their brain don't process that there are other ways to feel better besides dying.
Most people that try to kill themselves don't actually want to die, as recent studies show, but feel like death is their only way out at that point. But death isn't the only way out, which is why interference is usually very helpful and of course life saving. 
Someone else stepping in and really forcing them to see another side of things, with love and professional help, forces their brains to truly comprehend what's actually going on.
With a little work, a depressed person can re-balance those chemicals in their brains and continue a happy life, even though at one point all they could think about was the end. 
Without interference, too many people would try to escape this way.