I take it as their distorted reflection of themselves in that moment, starting to regain their humanity in their own eyes.

As their (assumed) partner said, "you don't look like a deer to me". Taking that with some assumed weight, we're looking at how this person sees themselves. Something weak, helpless, prey. They can't do anything besides try to keep surviving.

It's in taking the time with others, being treated as a person, they begin to feel it, see it once again.