In The Fugitive, when Kimble confronts Deputy U.S. Marshall Gerard in the drain tunnel, he says:
“I didn't kill my wife.”
Then Gerard says:
“I don't care!”
Why did he say that? It sounds like a ruthless thing to say to an innocent man.
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That the line sounds ruthless is the beauty of it; Gerard isn't concerned at all with guilt or innocence because that isn't his job. To Gerard, a judge and jury determines guilt, while his purpose is to do nothing more than track down Kimble and bring him in. This line also makes the ending sequence (where Gerard discovers the truth and tells Kimble that he believes him) that much more powerful ... someone who didn't care has come to care about Kimble's innocence when no one else would.
As a side note, this line was apparently (according to one of the producers) supposed to be "that's not my problem," but actor Tommy Lee Jones ad-libbed and produced the iconic "I don't care."
The TL;DR (too long; didn’t read) is that Gerard slips, falls, loses his gun, loses his radio and is now facing down Kimble—a fugitive from the law he is charged with capturing—that now has his gun and is pointing it at him. Gerard is cornered and doesn’t want anything to escalate.
While I generally agree with jlmcdonald’s answer, there is something really pragmatic about that line. Just think about that scene again via the script found here; just note Gerard’s line changed in filming as jlmcdonald’s answer points out.
INT. DOWNSLOPE CONDUIT - DAY
Gerard begins the tricky descent. Slips once. Recovers. Slips again…
…and tumbles out of control. GUN and RADIO CLATTER AWAY.
Scrabbling for purchase, he finally snags An overhead pipe. Gerard stabilizes. Sweeps his light to locate his Glock, lying down-tunnel. He eases toward it. But another hand gets there first.
It's Kimble. Face dark and desperate. Dangerous. Hand flexing on the pistol. They lock eyes for a beat.
I didn't kill my wife.
So, you didn't kill your wife.
Here, look at the full scene again. You might say him saying what he said is “cold” but to Gerard the only thing he knows at that exact moment is that a fugitive from the law now has his gun and is pointing it at him. He’s trying to be cool, calm, collected and de-escalate what is already a tense situation as best as he can.