Heh, ever see two other animals (eg bears) square off for a challenge? starts with eye contact.
It depends on the intention to bring to this. You seem to equate personal power with abusive power or dominance. Personal power is a calm, cool confidence and allows you to remain powerful without needing to impose it on others. You don't need to get others to submit but you can still hold your own. So, there is a third alternative between the two you have presented. You also do not have to have a "winner" or a "loser" when people first meet and while dominance heirarchies are important in human life (I've written about them on my blog), you do not have to live by those rules if you do not want to. Just have your personal confidence and step out of the game.
Being weak and wimpy is not noble, holy or pure and being strong is not being dictatorial, dominant, abusive, bullying or otherwise. I used to think being strong was to be abusive so I stayed away from it like the plague, but that really leaves you behind.
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