The Xbox 360 never had to make profit to be successful. The reason the product was introduced is that Microsoft saw itself going head to head with Sony in a number of markets, and so they wanted to undercut Sony's big cash cow, the playstation.

As long as Microsoft reduced Sony's profits more than Microsoft lost money, the mission was accomplished.

Ok, you pretty much stated my big problem with Microsoft. They don't have a great idea for a new product, but their competitor of the week has a product that they want to stomp.

What business does Microsoft have going after Sony?

They were head to head in a lot of places. Both wanted to create the next DRM standard, Sony was pushing Blu-ray so Microsoft pushed back, Microsoft wanted to push its software into portable devices, and Sony didn't want them there, and Microsoft was afraid that the Playstation would grow up into a general purpose computer in every household and undermine the PC market.

So Microsoft saw a company going head to head with them in a lot of key areas, and they decided to weaken the threat.

Costing Sony money would reduce the amount of money Sony could spend on other ventures. At least a subset of those "other ventures" are things Microsoft is actively interested in.

Disclaimer: I have no actual experience with either Microsoft or Sony when it comes to this sort of thing, so I might be way off target here.