Why are you speaking to me casually when this is the first time we have ever met?
"なんで初対面でタメ口なの？"
- Why are you speaking to me casually when this is the first time we have ever met?
- We've only just met, why are you talking so informally to me?
タメ口: casual speech; informal language
Why do you speak in a rude manner for the first time?
-> Why are you speaking to me so rudely when this our first time meeting?
-> This is the first time we have ever met, why are you speaking to me so rudely?
Why are you speaking to me so casually? We just met.
Why are you talking to me like we're old friends?
この場合、次のような言い方ができますよ。
ーWhy are you speaking to me so casually? We just met.
「なんでそんなタメ口なの？会ったばっかじゃん」
to speak to someone casually で「タメ口で話す」
ーWhy are you talking to me like we're old friends?
「なんで昔からの友達みたいに話しかけてくるの？」
old friends で「旧友・幼馴染み・昔からの友達」
ご参考まで！
アメリカ合衆国 
カナダ 
