Can someone explain to me why an identical twin is allergic to mushrooms and the other one is not? Also why a symmetric identical twin is more friendly/outgoing and speaks fluently while the other one is opposite?
Because your immune system, a highly complex interaction between countless cells, is not fully determined just by your genes or your environment. There is also a stochastic factor.
Without knowing any specific details, I can still answer that: because both allergies and personality are not (completely) dependent on nature, but to some extent on nurture.