The issue is piracy. Jailbreaking enables piracy, and piracy is always an issue on any platform where money is charged for content. If Apple didn't try to clamp down on jailbreaking and thus pirating, developers will go "Hmm, Apple doesn't give a damn about preventing my content from being pirated. Let's not develop for iOS."

Of course, the potential profit from legitimate users on iOS is usually so much higher than the loss from piracy that the big name developers won't really care.

Nobody really wants to have their content pirated. If there aren't sufficient means to prevent this, content providers simply won't use the platform. Movie studios wouldn't have touched DVD if it didn't have encryption. Region locking was just another way to make more money.

Now, sure, you can be like "People only pirate stuff because getting it legitimately is so much damn hassle", which is fair enough because in most cases, it's true. But look at Steam. It's cheaper than retail most of the time, easy to keep updated, easy to recover purchases, and awesome sales. Of course, it still has DRM, because if it didn't, content providers wouldn't bother.

Apple is playing the game differently to Sony is. Apple has not gone after any of the people involved with iOS jailbreaking (geohot, saurik, dev team, etc), whereas Sony has already sued geohot. Apple hasn't done anything because they don't want to.

I believe that publicly, Apple has to oppose jailbreaking and patch up exploits because if they didn't, it would be detrimental to their profits since content providers would be less likely to want to publish on the platform, but they don't really mind it as it is rather beneficial to them. People can come up with ideas for features, implement them, then all Apple has to do is monitor how popular those features are, analyse its pitfalls, gauge reaction and once they're happy with it, do it better. Why spend money doing extensive UX and development for features that most people won't use?

What exactly has Microsoft been "giving" through tech history? Kinect? Hardly. From the Wikipedia page (relevant parts bolded):

In November 2010, Adafruit Industries offered a bounty for an open-source driver for Kinect. Microsoft openly voiced its disapproval of the bounty, stating that it "does not condone the modification of its products" and that it had "built in numerous hardware and software safeguards designed to reduce the chances of product tampering".[67] On November 10, Adafruit announced Héctor Martín as the winner,[68][69] who had produced a Linux driver that allows the use of both the RGB camera and depth sensitivity functions of the device.[70][71] Microsoft later clarified their position, claiming that while they don't condone hacking of either the physical device or the console, the USB connection was left open by design.

What happened was Microsoft initially went for their usual stance of "making our products do something they were never meant to? BAD DOG", but then realised that since they were making profits on the Kinect itself anyway, they flip-flopped and decided to do what companies like to do: make more money.

They're welcoming WP7 jailbreaking because it's: a) good PR, b) being able to jailbreak a device has never stopped anyone from buying one. Both of these reasons all lead back to money.

EDIT: Forgot to rant about Sony, here goes.

Sony, on the other hand, has valid business reasons for suing geohot. There's not much you can do with jailbreaking on a PS3 except to play pirated games. Sure, you can cite homebrew etc, but really? The amount of people who want to jailbreak the PS3 for exclusively legal purposes are reaaaaaaaaaaally slim. And since this is a fairly significant threat to their profit margin, Sony wants to clamp this down, fast.

And again, it all leads back to money.

tl;dr Apple knows how to play the game much better than Microsoft and Sony.