Why did the Doctor give River his screwdriver?

In Silence in the Library and Forest of the Dead the Doctor sees River has a screwdriver.

RIVER: We can increase the mesh density. Dial it up four hundred percent. Make it a tougher meal.

DOCTOR: Okay.
(The Doctor uses his screwdriver to adjust Dave's suit.)

DOCTOR: Eight hundred percent. Pass it on.

RIVER: Gotcha.
(River holds up a sonic screwdriver of her own.)

DOCTOR: What's that?

RIVER: It's a screwdriver.

DOCTOR: It's sonic.

RIVER: Yeah, I know. Snap.

Then later they have conversations about it:

DOCTOR: Your screwdriver looks exactly like mine.

RIVER: Yeah. You gave it to me.

DOCTOR: I don't give my screwdriver to anyone.

RIVER: I'm not anyone.

DOCTOR: Who are you?
then later RIVER: What's wrong with it?

DOCTOR: There's a signal coming from somewhere, interfering with it.

RIVER: Then use the red settings.

DOCTOR: It doesn't have a red setting.

RIVER: Well, use the dampers.

DOCTOR: It doesn't have dampers.

RIVER: It will do one day.
(The Doctor takes River's sonic screwdriver.)

DOCTOR: So, some time in the future, I just give you my screwdriver.

RIVER: Yeah.

DOCTOR: Why would I do that?

RIVER: I didn't pluck it from your cold dead hands, if that's what you're worried about.

DOCTOR: And I know that because?

Then later he thinks

DOCTOR: Why? Why would I give her my screwdriver? Why would I do that? Thing is, future me had years to think about it, all those years to think of a way to save her, and what he did was give her a screwdriver. Why would I do that?

Then in the 2015 Christmas special the 12th Doctor gives River a screwdriver as a present.

DOCTOR: Happy Christmas.

RIVER: Really? I don't think you've ever given me a present before.
(She opens the box to reveal the sonic screwdriver she had in the Library.)

RIVER: Oh, it's a sonic screwdriver! How lovely!

DOCTOR: When I saw the sonic trowel, I thought it was just embarrassing, but, look.

I'm confused why did the Doctor give River his screwdriver?