Yes, it is annoying to have to log into two services because EA and Valve aren't playing nice to keep it on Steam and if everything else is already on Steam, why bother having to run another game service just to play one or two games. Kind of the GFWL argument.
However, there's more to it than that. EA's policies with Origin are worrisome and potentially seen as inrsurive and spyware. For example, Origin can look at your computer and the programs you have installed. I believe in the TOS they are allowing themselves to collect data and potentially sell it to third parties.
As a service, it's also kind of questionable in quality. Sure, Steam had a very rocky and poor start, but yet Origin is a service released in 2011 and yet it had a lot of issues in a time when Steam has been doing very well. People would have expected it to be further along I guess.
Then there's the fact of Battlefield 3. You would have to run origin to 'launch' Battlefield 3 which in pretty much just opening a web page anyway.
Then there's EA's banning policy. If you get banned on their forums, if that account is tied in with your games, you're banned from playing your games too. What's worse is that supposedly the moderators in the forums are very trigger happy with bans. This might even apply to the games themselves too, get banned from a game and you find yourself locked out of everything.
Speaking of customer service, a friend of mine bought The Old Republic at launch time and has yet to be able to play it. He's having some issue with his account. He's essentially locked out of his account and when he tried to recover it, they're only asking him one of the three security questions he had to create and the answer is case sensitive and he doesn't remember how the answer went. However, of the three security questions they're only asking for that one so he's completely locked out and he's getting no help what-so-ever from EA.
I'm sure there's more, but I can't think of it off the top of my head.