You answered your own question
Because sometimes it IS complicated. And you have to lie about it. Just because the relationship is worth more than the pride of "having" a girlfriend or husband. I was very happy with my girlfriend, but she was married, and going public would have caused serious issues. It would have cost me in my job, and in hers. And it would have been nice to be able to have been able to show him off in public, like others do in their husbands or wives or whatever. But it was just pride.
But you're right in that it's easier not to outright lie. I just tell very little of the truth, in a way that makes people think there's nothing deeper. And that suits me.