I found it strange...

[deleted]

I don't find it strange in the least bit.

Suppose an intruder broke into your home and murdered half your family. Would you stop and try and make a conversation with the murderer? I know I wouldn't. I think I'd have behaved exactly as she did in that situation.

I too didn't find it strange that "the woman" killed "the man", because, as Click_to_Register observes, she likely sees him as deranged, "descended" into less than an animal.

I imagine if the man had retained his civilized manner, unwittingly killed the bull, then been confronted by a well-groomed and fed dog wearing a collar, he would have reasoned an owner was nearby, called out, explaining that the bull-killing was a misunderstanding, and tried to hold off the dog without killing it.

Fail this, at least, confronted moments later after killing the dog by a yelling woman running up on him gun in hand, he would drop the axe and plead not to be shot - though I imagine such a plea would fail, because, as cowgoesmoo notes, the woman has just seen half her family killed, and likely couldn't restrain herself from avenging them.

The man's purpose in the film is simply to show us that she is no longer interested in civilisation. Like many with depression, she bemoans her isolation but when an opportunity comes along to escape it, she is more terrified of that than of the isolation itself (because she has become so used to it)

Depression is a vicious cycle

The clothes in the tree are probably another hint at the possibility of civilisation and she is both attracted to it but also repulsed by it

Writing itself is one of the most potent beacons of human civilisation......that's why the film ends when she decides to stop writing....because she has now completely abandoned civilisation

This is definitely not a science-fiction or fantasy-story. It's just a very artsy, philosophical, methaphorical movie. Therefore, the "man" symbolizes something (like others posted before) - the end.

I have the feeling too, that this movie maybe mostly symbolizing depression - or at least estrangement to other humans, humanity... the world... whatever.

I guess, the movie worked insofar as it did NOT sell itself as a sci-fi story or somthing.

The man symbolized something.
Also, you ask why she didn't spare him, why she didn't try to connect with another human.
Why, if you are truly isolated, would you try to befriend someone who has just brutally murdered someone whom you loved and depended on?
ALSO,
Notice that he killed the BABY of the group.
It takes a much stronger person to make means to survive and cultivate a "civilized" routine in the midst of isolation like this.
Perhaps this is to show that she is not "crazy".
I think this touches on our own internal struggles and how we unload our insanity onto others, much like war. The man had chosen to do this. At some point he made the decision that "this is not happening" and chose to descend into feral madness.
In stark contrast, the woman, we may have thought was crazy made the immediate decision to be logical. Investigate. Reflect. Observe. And then she took action. To survive.
We all have a different set of skills, at different levels. This is often the problem with reflective, introverted people; we are often attacked by those that operate on the "feral" setting.

I would have shot him just for kicking my dog. Anyway there could be only one

FACT: She killed the thug in the defense of others. Prove me wrong.