Female competition is when you are with a guy you like and you look around, see that you're the prettiest girl in the vicinity and feel a huge sense of relief that there's no one to take the attention away from you. (Female competition is a result of women feeling like their greatest sense of self worth , identity and influence comes from their sexual appeal to men. Many women don't even realise they are feeling this way and it's a subconscious thing, but they notice themselves getting jealous when they see other women who they think men would find sexually appealing.)
Sexual objectification doesn't get oppressive until it is done consistently, and to a specific group of people, and with no regard whatsoever paid to their humanity. Then it ceases to become about desire and starts to be about control. Seeing another person as meat and fat and bone and nothing else gives you power over them, if only for an instant. Structural sexual objection of women draws that instant out into an entire matrix of hurt. It tells us that women are bodies first, idealised, subservient bodies, and men are not.
When female stories are muted, we are teaching our kids that their dignity is second class and the historical accounts of their lives [are] less relevant. This lowered value carries over when women face sexual objectification and systemic brutalization from inside and outside the community.