The first time Ladybug and Chat Noir met, they worked together to defeat Stoneheart. They swore to protect the citizens of Paris and keep the city safe.
The city loved them.
The second time the two Miraculous wielders met there was tension. They tried to work together but something was off. Chat's baton would miss, Ladybug's yoyo would tangle, the two could not seem to put a proper plan together. No matter the difficulties, the two stopped the Akuma and Ladybug purified the little butterfly to the cheers of the citizens of Paris.
The third time they met was the worst yet. The two would barely talk to each other, easily getting in the way of one another and causing the fight to drag on longer than it ever needed to be. When they did talk, it was only to argue over whose fault it was that the Akuma had slipped through their fingers again. By the end of it all, Chat managed to get the item away from the Akuma and released the butterfly. But he couldn't do anything else.
Chat Noir could not do anything in the eyes of the city. All they saw was Ladybug purifying and fixing the damaged the Akuma had caused.
Chat was destructive. He got in the way of Ladybug. He only caused more problems than there were to begin with. Even when he helped there was little thanks given to him.
They all cheered for her.
It was not fair.
The city love Ladybug.
They tolerated Chat Noir.
Chat Noir knew he could do better than Ladybug.
The fourth time they met they acted on their own, each trying to get to the Akuma first and defeat it before the other gets the chance to. Chat got to it first. He took this chance to try something.
He used Cataclysm on the poor little butterfly.
The butterfly died, and along with it all the evil feelings that were used to create the Akuma. His plan worked. But not fully.
Taking one look around him, he saw the damage done to the city was only half repaired. Luckily the Akuma had still been fresh and hadn't cause much damage to the city but there was still some and that was all the citizens would care about. Chat Noir stopped the Akuma but didn't fix the city.
Not like Ladybug could.
"You should have waited for me. We're supposed to be partners."
"Then why can't we work together correctly? Why do they only care about you?"
"The city cares about both of us."
"They only cheer for you, never for me."
"It's not important who they cheer for, what's important is that we keep this city safe as partners."
"It would still be nice to be appreciated, to be seen as your partner and not as a nuisance"
If he couldn't be a good partner then he would be her rival.
Maybe even her enemy.