Because your wife is assuming it will be an opposite sex partner and it appears you don't know if your wife will be ok if your secret partner is of the same sex. The fact that you posed the question tells us there is a possibility that she won't be ok with it and in that case it should be discussed beforehand. Just because you have agreed it will be a secret now doesn't mean problems won't arise later where disclosure might become necessary.

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Put me on wheels and I'll turn tricks.

Clever? Nah, I ran out of that years ago. But if you find this, let me know, k?
"The road goes ever on..." ~ Tolkien

In memory of my friend skip...
Go then, there are other worlds than these