why is it wrong to say "estoy feliz."?
though we say "Estoy alegre.", why cant you say "Estoy feliz." ?

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Answer

Generally 'feliz' and 'alegre' are synonyms. Though, I use 'cheerful' to mean 'alegre' in Spanish, because I could say 'Mi amiga es una persona alegre' (My friend is a cheerful person), it's not a temporary situation, she's like that; but 'Mi amiga es una persona feliz' (My friend is a happy person) probably because she's having success with her life. For me to be happy is a process, to be a cheerful person is a way of being. 

P.S. This is my way to make a difference between them. I'm not sure if it's okay though. :)

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Both are correct :)
Who told you that it's wrong??

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Both are correct. You can say "Soy feliz" It means I am a happy person (all the time) "Estoy feliz" means I am happy at this moment.

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私は幸せです!  私は嬉しい  It's the same or not? en español "estoy feliz"  "estoy alegre"

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