Hardcore gamers like me don't like the way they cram the Origin software down everyone's throats.
It started with Battlefield 3 back in 2011. BIG hype and anticipation for this game, but on PC, you suddenly HAD to plug in to this Origin system in order to play the game, and on consoles the game had an "online pass" that everyone had to pay $10 for if they got the game used instead of buying at full retail... that just doesn't happen with other console games.
Since then, they've been dangling the franchises they have control over (Battlefield, Crysis, Mass Effect) in front of gamers with strings attached to things like first-day DLC and other little "rewards" for people who buy for full price on the first day of availability. They've also taken a strong stance against selling games at reduced prices like we get with Steam Sales.
In a nutshell, EA is kind of at the forefront of this creepy movement in the gaming industry to get gamers to pay more money for their games. They're trying to get everyone used to a world where nobody gets a game at a reduced price because it's used or it's been out for a few years so the price is dropped... instead, they want a world where all gamers pay full price for every game they play, which is a big deal because most full games these days sell for around $60 when they first come out.
That's why people don't like EA.