One thing that stood out to me during Episode 39 of Utena is that Utena and Akio seemingly tried to open the Rose Gate in different directions.
Akio as he is slashing and stabbing at the Rose Gate is obviously trying to open it by applying force towards it, he is treating the door as a push door and in comparison to Utena is as well using a tool or well a weapon in an attempt to get it open.
Utena, and of this Im admittedly not completly certain, seems to be based on her posture trying to pull the door open.
The first noteworthy difference between push and pull doors is the amount of difcficulty one has opening them, push doors being much easier to open due to the applied force following the objects motion while the force applied during pulling goes into the opposite direction.
Now while there are no actual regulations for what direction a door should open to when, but generally speaking a door is pushed open when a room or house is being entered from the outside and pulled open when leaving a room or a house.
So Akio is not only using the method which costs less effort, he is trying to enter into something, the space where he believes his princehood lies to continue a fairytale in which he is the knight in shining armor, a restricted room waiting for him to get inside, to leave what he views as the outside, the reality he is complacend in and does sees as such, his general space of being and Utena is in comparison trying to leave a confined space around her to reach the outside with a method more strenous, of course behind the Gate lies Anthy.
And as we then see Utena opening Anthys coffin, it is arguably a sliding door. Now, sliding doors generally have the effect of seperating one singular space into two seperate ones, in this case seperating Anthy from a world, a space she is part of, then the floor breaks, we see the space well and truly seperate itself from the platform.
When Anthy then leaves we are faced with two new sliding doors, the elevator door in Akios office, closing behind Anthy as the space of the elevator seperates itself, not simply by closing but by moving itself downward which I do find to be reminiscent of Anthys fall, leaving the tower, leaving a point high up above, surrounded by nothing but the sky to get to the ground upon which to walk on and then Ohtoris gate, seperating the place from the rest of the World in the end Ohtori is part of the world, but not the whole of it, much more of it isn't, the gate does not close, there are many more who can leave or enter, Anthy could very well turn around and get back inside, but she chooses to walk way.