So you are a modern woman; great job and education, a car maybe, got your own place, all your ducks in a row.
Ms Independent precedes your name. You have taken in further – you want a Strong Independent man.
But your translation for “strong and independent” happens to be as follows; He doesn’t have to open the car door for you (the door isn’t broken neither is the car new), doesn’t have to pull up your seat in a restaurant (you aren’t weak), doesn’t have to pick the bill (you are an independent woman, silly), doesn’t have to call you up (shared equal responsibilities). And so on.