"You chose a valuable hostage," he said as they ran.

The "why" was simple enough: a Federation medical officer would make a valuable hostage, indeed.

Even if they lost their lives, the others were still valuable hostages.

He's a valuable hostage and they'll want to hold onto him.

And they're desperate enough to see you as a valuable hostage.

"He is the most valuable hostage they could hope to hold," Picard said.

As to the 'why', they would have made potentially valuable hostages but the perpetrators clearly wanted them dead.

Now, with your own tongue, you have made yourself a valuable hostage!

He tried to comfort himself with the realization that she made a valuable hostage.

You can't kill me because I'm a valuable hostage, remember?