New Reverse Compatible Titles announced :)

Its a good strategy for Microsoft as that will promote sales of their newer, more expensive products and slowly wash out the old ones that they just want gone from the shelves. At the same time I'm sure the purists and "veterans" will be more provoked to buy a new console because they will be able to play the games they love. At the same time, some people who already have a One will want to buy those old 360 games to relive their memories or get some sort of nostalgic satisfaction.

So I'd say its a win win situation on both sides, this also means game developers can feel a little more comfortable knowing that even if they still release an old gen title, that there will be people who buy it.
I also think that this will help to convince more and more people to start buying the Xbox one, as they'll see that their favourite games that they are currently playing on the Xbox 360 now, they won't have to give up.

There are a lot of titles on the 360 that people love still, and I do think that's why the Xbox ONE hasn't been as successful as Microsoft originally thought it would be.
I think this should just be happening more frequently, ideally. If they focus on letting us use some of our 360 titles, that pushes the aftermarket of the 360, leading to more sales overall since new consoles sold are probably going to favor the xbox one for a little while since you may as well, so iffy competing with your own console, lol
If competing with their own console as you put it, makes more and more people turn round and start to buy the Xbox ONE then Microsoft will be more than happy.

Not only Microsoft, but the players that bought the Xbox ONE from release that are now just sat waiting for other gamers,,and the game developers to catch up.
The only reason that I don't necessarily agree with that is because there are still a large number of unsold 360 consoles available, and ideally, all of them get sold and the product continues moving, especially considering how many games need to be sold still as well. They are balancing two very strange desires.