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As usual, retards completely miss the point of Silver's character even though it's literal spelled out to you during the course of the game if you actually payed attention instead of just mindlessly spamming A.
When Silver calls you "weak", he isn't saying you're a weak trainer, he's saying you're a weak person. Specifically, weak for caring about your Pokémon and treating them with respect. This is all made clear in the first two interactions with him at the very start of the game.
The most obvious tell however, is when Team Rocket is brought up. He also refers to them as weak. Why? Team Rocket are weak because they have to resort to grouping up and ganging on vulnerable people/Pokémon in order to get shit done, whereas Silver does everything himself.
Silver views himself as stronger than you because he is purely focused on being the stronger trainer. He does not care about other people, he does not care about the world, heck, he doesn't even care about his own Pokémon, they are merely tools to make HIMSELF excel at his primary goal; being the strongest trainer.
That is why he calls you weak every time you beat him. He thinks he can become the strongest trainer with just brute force. However, if you paid attention to the dialogue, like I said before, you would notice him start to doubt himself several times during his journey to the League. The first time is after his encounter with Lance, where he questions his way of going about things. It's not enough to change his mindset just yet, but the seed of doubt has been planted in his mind. Then, after your final battle with him before the League, he finally realises why you have been beating him every time. What you possess and he lacks.