The problem with asking for an antonym is that most words have more than one nuance or meaning, so antonyms can branch off into more than one direction – and sometimes even several.
In the case of addiction, I can think of at least two senses of the word:
There's addiction as a chemical, biological, or psychological dependency, usually regarded as detrimental to one's well-being (e.g., drug addiction, sex addiction, gambling addiction).
Then there's addiction used in a less scientific way, where it describes more of a rabid obsession than a true dependency (as in, addicted to fishing, golf, or romance novels).
The NOAD describes it like this:
So, as for antonyms: when talking about the latter usage, we might try words like:
indifference, apathy, disinterest
Bob is addicted to bowling, but his wife Mary is indifferent about it.
My daughter had a Pokemon addiction in grade school, but she finally grew out of it, and feels only apathy now.
But when we are talking about the former usage – such as someone's bout with alcoholism, or struggle to quit smoking – words like disinterest and dispassion don't work very well as antonyms. I'm more inclined to suggest words like:
independence, autonomy, freedom
Paul has been free from his nicotine addiction for six years now.
I thought Mary had finally gained independence from her alcoholism, but it seems like she can't stay on the wagon.