EDIT: Some things that I regret saying.
Okay, So the way I see it. My opinions only, I don't claim to work for BioWare/EA I just make them laugh with gifs.
First of all, I'm not blaming anything on BioWare, but mostly EA.
When the development of DAI started, the older consoles were still popular. Hell, the development started even before the new consoles were announced. Releasing it for the older consoles as well as the newer ones was a sensible choice because a) More people buying the game, meaning more money, and happier customers. Imagine the storm that would have followed if they would have announced the game only for the newer consoles and PC back then. It would not have been pretty. After their initial announcement and realization that this decision was risky as hell, they couldn't retract the statement due to backlash and the fact that they were already working on the ps3/360 version, and scrapping it meant that they would also scrap the possible extra cash they were going to make. (this was probably EA's idea as devs need to get paid, yo).
EDIT: It wasn't partly due to money, but also technological reasons. It's difficult as hell to port over a next-gen game to a 10-year old console and have it to work as it should. Basically see what Bryan has said a couple dozen pages in.
However, anyone who has played the game on newer consoles can see that the game suffered due to the fact that they had to spend resources on a ps3/360 version of the game on the side. Also my guess would be that the game and the DLCs didn't sell all that well on the older consoles, and it just simply wasn't profitable in any shape or form. (plus technological reasons) As much as I hate EA's money laundering antics (from two years ago), games aren't made from sugardust, but money (meaning: devs have to get paid, not just EA). So the most logical decision to make here to keep everything afloat is to stop developing for the older consoles alltogether. The newer consoles get MUCH better quality DLCs and content, BioWare and EA has money, everyone is happy except for everyone who bought the game for older consoles and was wounded in this failed experiment conducted by EA. I take this back. You buy a game for a 10 year old console at old risk. You can run DAI on a laptop from 2012 on lowest settings.
I have mixed feelings about this issue, but I totally see where they are coming from and WHY they ceased to care about the older consoles. Answering the question of "Should they even have developed the game for older consoles in the first place?" is VERY tricky, because as evidenced by the internet, it would have been a mess no matter what they would have done. (plus all the technological reasons completely slipped my mind, because let's face it I was out of it when I wrote half of this crap.)
What I don't really condone is EA using this opportunity to get even more money from game sales. Yes, I know, what I said above about money, but these people have already purchased the game (+ the DLCs) and the least you can do is give them a free game upgrade to the newer consoles, then host a contest to win a couple of xbones/ps4s.
(Brojo explained the server thing so free upgrade is out of the question.)
tldr EA took a risk which didn't pay off all that well and I totally understand why they did it.