I'm attracted to qualities in a Woman that would turn off a typical guy. I find when a Woman is an independent thinker, her own person, has her own passionate interests, is a big turn on! If a woman is ambitious, maybe a business owner, owns her own home or has accomplished something to call her own and doesn't put up with BS or disrespect from others and is straight forward is awesome! I love that!
The thing I've found is that when 2 people are like-minded in this way it's hard to come together even to get to know each other, especially as a Male looking for these qualities in a Woman...becuz a Woman who's independent, has her own thing going on...doesn't need a man, BUT wants a man who can be a partner, someone who challenges her on her level isn't going to easily let another into her personal space and vice-versa...I find there's an aloofness, a standoff-ish vibe towards getting to know someone who's interested in her.
Not really a question, just something personal I wanted to share.

Is being independent extremely important to you, but at the same time wanting a sense of companionship with someone who feels the same?

Arrh, yes. I fully agree. I've loved a number of strong willed woman. Exciting, challenging, only dangerous when you're in their sights. But a mistake I'll happliy keep repeating.

When the gods wish to punish us, they answer our prayers.Oscar Wilde