What is Kylo trying to achieve in the tug of war, anyway? Presumably he’d like the troop carrier to be able to fly off. Despite this, he appears to be also trying to pull it towards the ground, like Rey is, just in a different direction. I suppose the whole ‘trying to push Rey’ thing covers it - but that explanation comes later in the movie, so in the actual moment it just seems strange.
I always interpreted it as Kylo being blinded by his emotions, almost like a little kid - Rey wants the transport, so Kylo doesn’t want her to have it.