I believe what you are encountering are instances like "Canadians for choice", or "Republicans for choice", or "Feminists for choice."

In this case, "choice" is the noun, and its meaning is "the right, power, or opportunity to choose", and such "Canadians for choice" are slogans that emphasize their goal to promote the right for "Canadians"(in this case) to choose as they like.

Another instance of usage of "for choice" is in the idiom "spoilt for choice", which means:

Having such a selection of good choices, that deciding which one to pick is difficult.

Example sentences could be:

I was spoilt for choice.
Adam was a complete supporter for choice

I'm not quite sure what you are encountering. I can think up of two usages for "for choice".

"Canadians for choice", or "Republicans for choice", or "Feminists for choice."

In this case, "choice" is the noun, and its meaning is "the right, power, or opportunity to choose", and such "Canadians for choice" are slogans that emphasize their goal to promote the right for "Canadians"(in this case) to choose as they like.

Another instance of usage of "for choice" is in the idiom "spoilt for choice", which means:

Having such a selection of good choices, that deciding which one to pick is difficult.

Example sentences could be:

I was spoilt for choice.
Adam was a complete supporter for choice

It's not an idiom, so there's no origin.