My one-sentence summing-up of my problems with EA: business decisions which directly result in poor game design.
— Silas Humphreys (@McNutcase) April 5, 2013
Let's look at that in detail. To do that, we have to understand what EA is, and is not.
EA is a publisher of computer games. What a publisher does is provide funding for development, set deadlines, and arrange distribution. The provision of funds and setting of deadlines is where their power comes from. EA is not, in general, a developer; it owns multiple development studios, but it doesn't generally have direct control over them. The developer's role is to make the games.
Now we have to look at what EA does that makes people dislike it. A lot of these behaviours make sense in the context of what EA has gained most from, so we have to be aware that for many years, the lion's share of EA's profit came from licensed sports games.
The first thing that annoys gamers is yearly release schedules. Not that any gamer would normally object to getting a new game in their favourite series once a year, but the yearly cycle puts pressure on the developer. For a sports game, a yearly release schedule makes sense; players change teams, and you can spend that year incrementally improving the polish of your simulation. A 2013 football game won't look or behave significantly better than a 2012 one, but compare it to the 2003 one and it'll be a massive improvement in both graphical and simulation fidelity. Sports games rely on improving technology (which is fairly cheap, in terms of creativity) and accurate data entry. Most other game genres rely on content creation; someone has to think up what your city looks like, create each dungeon, and so on; the bulk of your development time is eaten up by content creation, rather than the predictable technology improvement. You could try adding more people, but this bulks up the budget, results in the content being in smaller chunks as it's very difficult to have two people working on one level simultaneously, and is at best a wash. Deciding on yearly releases (a business decision) leads directly to the detriment of game design.
Then we move on to DLC. While some DLC is a good thing (what used to be referred to as expansion packs), what bothers people is cosmetic DLC, paying to win, and so on. This is the petty stuff where people will ask "Why wasn't this in the game anyway?" and it's not really something I can explain, beyond it being a way to price something at below most people's impulse threshold and have it be profitable. "Pay to win", overpowered items for which one can pay real money, are poor game design in a single-player game, poor game design in competitive multiplayer, and remain poor game design in cooperative multiplayer due to envy.
Now we hit the big issue: DRM. DRM is definitely a polarising thing; people who've not been inconvenienced by it may not see the problem; people who have been inconvenienced by it will figuratively tear the heads off those defending it. It's certainly an issue when it prevents legitimate buyers from playing the game (witness Sim City, Dragon Age 2, and countless other examples) and it's more of an issue when it's poorly implemented. I don't know that there is a way to implement it well, but forcing a game to always be online is generally a bad idea (many people, even in the affluent USA, do not have access to stable, high-speed internet connections) and out-and-out lying about why the game requires a connection is a definite bad move. In general, EA's DRM has resulted in bad experiences for buyers, and has not provided a compensating convenience.
And on the subject of convenience, one of the common complaints about EA is that their products aren't always available via Steam. Steam is about the best DRM I've met; it's unobtrusive, and it provides great convenience. I can buy a game on Steam from my cellphone, and have it installed on my computer by remote control. In most Steam games, I have access to a web browser in-game if I get stuck. It periodically runs ridiculously deeply discounted sales. While I haven't actually used EA's Origin myself, I've heard many complaints about it. The root of EA's refusal to put flagship products on Steam is a desire to avoid having a middleman take a cut; but that's short-sighted. It would be like refusing to sell books via some bookstores, when some buyers simply won't go into the stores you do sell through. While Steam would undoubtedly reduce sales via Origin to some extent, it would also result in sales that EA would otherwise not make.
In some ways, EA's situation is similar to Apple's shortly after the ouster of Steve Jobs; the margin years. EA is chasing short-term gain, trying to improve its margins, and in doing so is killing its volume. No amount of margin can compensate for low volume of sales, but volume can more than make up for a low margin. Sadly, I doubt EA will find a person who understands that to lead them.