Can someone be a player and introverted at the same time, and can someone be extroverted but completely incapable of that?

Jean-Marie_Céline
Can someone be a player and introverted at the same time, and can someone be extroverted but completely incapable of that?
I know it sounds weird, but hear me out.
My father is a person you might call a ''player'', but up-close he's almost shy and reclusive. He doesn't like big crowds and barely raises his voice, and he often stutters. I thought he might be like that because of his age, but people confirmed to me he was like that even when he was my age.
Instead I'm much more istrionic, make myself no problems to smile and hug people, talk with a deep, raspy voice, and I like to mix in with people. But I can't understand at all if someone is flirting with me, and I've been warned that some people did try to flirt with me or mistook my friendliness for flirting. I got told that my grandfather was the same as me, and like him I have zero romantic interest in other women that aren't my wife. I've gotten called a ''block of wood'' because of that, but I don't agree because I move, smile, laugh, and hug.
That's one heck of a paradox, isn't it?
Can someone be a player and introverted at the same time, and can someone be extroverted but completely incapable of that?
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