Opposite word of "addiction"
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.
You're probably referring to the term used with a hyphen: "de-addiction." You can easily find this one in the dictionary.
Without the punctuation, it's a bit tricky to read and recognize.
This is a specific term used in health and substance-withdrawal fields.
Various comments and answers have already stated the majority of this, but I think a complete answer needs to have it all:
Basically, a word can have many antonyms, depending on which definition - or which part of the definition - one intends to negate.
When "addiction" refers to the process of becoming addicted to something, the antonym would indeed be de-addiction - the process of becoming no longer addicted.
"Addiction" also often refers to an uncontrollable desire for something. We can negate this one way by using aversion or revulsion (although those are more directly antonyms to attraction) - an uncontrollable desire to avoid something.
We can negate this another way by using indifference or something similar - the lack of any particular desire for something.
When "addiction" refers specifically to the inability to not use a substance, possible antonyms are independence or freedom. (I think the former is particularly good here, because drug addiction is commonly called chemical dependence.)
Finally, one can always use non- to make an ad-hoc antonym for any noun - non-addiction is the state of not being addicted, whatever "addicted" may mean in this context. This kind of construction might be useful in certain kinds of writing - for instance, if we wanted to describe the participants in a controlled study as either addicts or non-addicts.
If the term addiction is used in the sense of the disease or state of addiction (as opposed to the process of becoming addicted to, or dependent upon, something), one good antonym would be sobriety.
Jo got her six-month chip, recognizing a half year of sobriety.