Whether we consider competitiveness as all right is very context-specific. So
Michael Phelps can be competitive at the Olympics and we'll cheer him on. But, during a board game at home, to say, 'Whoa, he was just really being competitive' - that's not supposed to be a compliment. As a woman, being told you're competitive is even often more pejorative because it's meant that 'Oh, she's kind of bossy'.