EADM and Origin share code yes they are not the same, thats like saying steam is WOW.
We know a lot of the details, about what happend
1. Around the time of DA2 Valve changes it's Steam publisher contract that restricts ingame stores and requires all things available in any store must be available via steam it also requires price matching with other stores etc.
2. Valve and EA have a very public dispute over this and EA announces it will no longer release it's first party games on steam if they have DLC planned after DA2, DA2 is very publicly removed from steam the day DA2 DLC hits. Valve cite breaking of the publisher agreement due to an ingame store. Shortly before this Crysis 2 was removed for the similar reasons.
3. Origin was released less than a week before C2 was removed and just over 5 weeks before DA2... Valve claim it was due to EA request as they are now Origin exclusive EA continues to sell it through other platforms and posts statement calling them out...

Now consider the contract changes occurred 2-3months before Origin opens. EA has no rival to Steam and therefore no... leverage shall we say... in contract negotiations. Valve pretty much demanded a cut of all profits related to games DLC even if their servers weren't providing the content and Valves cut is thought to be 20-50% of any item sold through it's store (yes really). EA had a lot of reasons to rush out Origin before it was originally planned to release.

Stopped reading after this nonsense statement. No reason to argue with that 'logic'.

BULLSHIT! Do you remember the Valve downloader before there was steam? Seriously! Before there was steam there was WOW a crappy little downloader with no store that was there just to download Valve games and do some simple matchmaking (read EADM) then Steam was released it added semi decent matchmaking, a store, and that was about it.(read Origin) it took 8 months for us to get news friends etc added to steam. at least Origin had them at release.
Oh and a quote from an article 6 months after steam released "Steam sucks" sound familiar?

WON, not WOW.

whoops good point didn't notice i'd typo'd all those times >.<

Ahh, after TAC that maks more sense.

But you're still talking about a less than a year timeframe. And comparing an 8 year old client with no similar precedent to the 'rerelease' of EADM (Origin), a 2008 client, so it took 4 years to get what you have now. (although granted, they seem to be putting in more effort, finally).

As I said theres fair chance Origins release was an attempted bargaining tool for EA if the changes to the contract hadn't occurred I doubt this very public beta would have either as is. BF3's matchmaking was pretty obvious in it's rushedness it's now much better and origin itself is improving they just need to clean up the store and put demo's on the game page (rather than free games section) and make them removable....

you're fishing.

the only thing Origin has to do with Valve is the fact that Steam is so successful and EA wants a piece of that cake.

the whole DLC for EA games on Steam issue is unrelated. EA used that as a pretext to remove their latest games from Origin's main competitor (Steam has a 70+% market share...) in order to boost the popularity of Origin, and now they're releasing their new games as Origin-only (FIFA 12, BF3, NFS:TR, ME3).

How am I fishing it's a matter of record Origin was a suprise announcement shortly after Valve altered their contracts.

Also EA never removed a game they still offer all their catalogue to DD's steam removed them due to "breach of agreement" the letters are in the wild. Origin only is a bargaining chip they can go up to Valve and go "We'll happily allow you these games but they of course have our ingame store and matchmaking as part of them" Valve doesn't allow these in non-valve games so they don't get released on steam.

::edit to add::
You'll note games with neither are available on steam and new EA games are still released on there if they have neither.