Por que o título “The Karate Kid” quando eles estão usando Kung fu?

Porque é um remake de um filme com o mesmo nome e eles não querem perder a popularidade do filme mais antigo. Se você assistiu a ambos os filmes, notará que ambas as histórias são bem parecidas, substituindo apenas o Karatê pelo Kung-fu e mudando a localização.

A Sony, em determinado momento, pensou em mudar, mas não no final:

Despite maintaining the original title, the 2010 remake does not feature karate, which is from Okinawa, but focuses on the main character learning kung fu in China. Chan told interviewers that film cast members generally referred to the film as The Kung Fu Kid, and he believed the film would only be called The Karate Kid in America, and The Kung Fu Kid in China.

Sony had considered changing title of the film, but Jerry Weintraub, one of the producers, rejected the idea. Weintraub was also the producer of the original Karate Kid. - Wikipedia

O filme de 2010 The Karate Kid é um remake de um filme de 1984 com o mesmo nome. Em esse filme, Daniel aprende Karate e participa de um torneio .

A partir daqui :

Miyagi proposes that Daniel will enter the Under-18 All-Valley Karate Tournament, where he can compete with all the Cobra Kai students, and he requests that the bullying should cease while Daniel trains. Kreese agrees to the terms, and warns that if Daniel does not appear at the tournament, the harassment will resume on Daniel and Miyagi.

Miyagi begins Daniel's training by telling him that Daniel is required to commit unequivocally to Miyagi's curriculum, and to obey Miyagi's every instruction, without question. After Daniel agrees, Miyagi assigns Daniel to complete various lengthy, menial chores that appear to have nothing to do with karate.