Did she do something wrong? Why was he glaring at her?

if you read other manga its usually a guy gives out his hand to let the lady ride the carriage

He wanted to help held her hand when she get up to the carriage, but right when he was about to held out his hand for her, Penelope turned her head away and get up to carriage by herself.
Even after this, Penelope still did not realise anything. I mean, she knows they have bad relationships, and she thinks he hates her a lot.
No way in a million times Penelope would ever imagined he would over a hand for her to the carriage....
So, he was annoyed that Penelope just ignored him.... lol....
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You know Tsundere & Kuudere right?
Now, this guy is the epitome of a guy with a personality that’s a mix of both Tsundere+Kuudere=30%+70%.
But that personality will come out more clear in the future chapters.
If the older brother is like that....
The younger brother is the hotblooded, childish 100% Tsundere type....
this young boy is the type of guy who lifts up the skirt of a girl he likes, or pulling the hairs of the girl he like.... Yeah... he is just a snotty little boy....

Thank you