she's left-handed

A young married couple are taking a nice stroll down a long and rather winding road. There was a long way till they got home and there was plenty of time to have a long drawn-out conversation, so the wife decided to ask her husband a question she had on her mind for a long time:
Wife: "If I died, would you remarry."
Husband: "No, I love you too much to get married to a different woman."
Wife: "But you love being married, don't you? So honestly. You'd get remarried wouldn't you?"
Husband: *sigh* "Yeah, I guess I would get remarried eventually"
Wife: "Would you and your new wife live in our house?"
Husband: "Yeah, where else would we live"
Wife: "Would you take down all the pictures of me and you together?"
Husband: "Yeah, it would be very discourteous to her not to. I'd still keep the ones of me and you in my private drawer"
Wife: "Would you two sleep in our bedroom?"
Husband: "Yeah, where else would we sleep?"
Wife: "Would she use my golf clubs?"
Husband: "No, she wouldn't be able to. She's left-handed!"
Wife: ...
Husband: "SHIT!"
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explanation
Him saying that she's left-handed implies he already has someone to get remarried with, meaning he's been cheating on his wife.