As far as I know, this is the situation:
There are two main versions of the Sims 3, the original which was released on PC back in 2009 and the updated version which replaced that in 2012 (correct me if these dates are wrong).
If you purchased the game before the new version was released you can play truly offline, not what EA claim is offline, I have this version and can easily launch The Sims 3 games without having to be online or logged in to Origin.
However, if you have the newer version (post-2012) then, unfortunately you cannot do this, you will need to log in to Origin each time you want to play and then go offline from there.
Though this is not truly offline you can argue it, rightly so, with EA till you are blue in the face, but they will stick to their guns claiming this logging in to origin to verify the game is still offline.
Personally, I believe that this is very unfair for many reasons, they even advertised and promised that the Sims 4 would be offline, but that is not the case.
Some people have managed to work around the Log In requirement by launching the games as an administrator or from the .exe file, there are a number of ways to to this but with each updated version of Origin its becoming harder and harder.
They are clamping down on their customers using their own games, which have been rightly bought and paid for, the way they wish. And this is honestly, very unfair.
I read that back in 2012 a law was passed to make digital content more like physical content in that once a customer purchases it they can do what they please, whether thats modding or reselling it. However, it is funny that the same year this was passed that EA released a more restricted version of the sims 3, not allowing such activities. The law states that the product is purchased by the customer so can be used however they wish, yet upon installing the sims 3 games you can read in the first few lines that EA have worked round this by stating that the games you have purchased are merely licenses and not in any way your own property.
If you happen to contact Origin regarding any activation or code related issues, do be warned as they will try best they can to replace your pre-2012 game code with the newer one, to ensure you get stuck as everyone else is on here.