The phrase "agonizing choice" means a difficult decision that causes a lot of mental or emotional pain. It's a choice that is really hard to make because it involves sacrificing or giving up something important. Full definition
Finally, in a more disturbing vein, faced with the choice of allocating personnel and resources toward a mode of medicine benefiting only a few, and allocating those same personnel and resources toward a mode of medicine which would benefit many, one should opt for the greater good for the greater number — although this would be a very agonizing choice for any triage officer to face. (religion-online.org)
We've tried to present you with agonizing choices as you navigate your way through the sequel and built that into a bigger, much darker story. (pcworld.com)
One of the most agonizing choices an entrepreneur inevitably faces is whether or not to close their business. (inc.com)