I think you have to express to your wife that you want to learn Mandarin because eventually she will find out about your mandarin language learning software or podcasts.
Possible reasons you can use to convince her to teach you.
1) You want to get along with her relatives better esp. granny.
2) You want to provide your future kids with a total Chinese environment at home.
3) You want to understand her better by learning the language and the culture behind it.
4) You want to eventually start a biz that services the Chinese community. (I know a white contractor who services the Chinese community in California. His Chinese wife brings all the contacts and builds the relationship and he provides reliable, quality service. Apparently he does well and most of his biz is with the Chinese community)
5) You want to be able to order from the secret menu that is only provided to Chinese speakers who go to Chinese restaurants in the West.
All of the above reasons will give you some good conversational ability that will serve you well in China.
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