だって is a colloquial combination of the 助動詞（じょどうし） (auxiliary verb)
だ, and the 副助詞（ふくじょし） (adverbial particle) とて in Japanese (a combination of the particles と, and て). It has a wide range of uses, but primarily exclaims that something is the ‘premise’ for whatever has been said, or will be said next. This ‘exclamation’ is usually translated as ‘I heard’, ‘cause’, ‘but’, or ‘even if’. The meaning that will be conveyed is determined primarily by where
だって appears in a sentence.
When placed at the beginning of a sentence,
だって highlights the speakers (usually) displeasure about something that has just been said, before following it with an explanation or counterpoint. This
だって is quite similar to
でも.
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え〜行（い）きたくないよ。だって、俺（おれ）の元（もと）カノも誘（さそ）ったんでしょう？
Awwww maaaan I don't want to go. It’s because you also invited my ex-girlfriend, right?
だって、サメとか怖（こわ）いもん。
It’s because I'm afraid of things like sharks.
At the end of a sentence,
だって is used to express hearsay, in a similar way to ‘I heard that’, or ‘it was said that’, in English. In these cases it will be preceded by なん. なんだって always appears after a noun, or a phrase that has been nominalized (with の or こと).
-
レムの実家（じっか）は農家（のうか）なんだって。
I heard that Rems' family owns a farm.
キリコは明日（あした）から一週間（いっしゅうかん）休（やす）みなんだって。
I hear that Kiriko will be on break for a week starting tomorrow.
When used directly after a noun, だって has a similar nuance to the だって that appears at the beginning of sentences (emphasizing what has come before it, in order to explain further). This comes across as
でも, and may not be used with なん.
The 副助詞（ふくじょし） (adverbial particle) とて itself is an abbreviation of expressions like と言（い）って, and と思（おも）って. だとて (the full construction) may also be used, but is almost always replaced by だって, as it is far easier to say.
When used at the beginning of a sentence, もん or もの will often come at the end of that sentence, in order to strengthen the opinion given by the speaker. This is more commonly used by women and children.
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私（わたし）もそんなもの食（た）べたくないよ。だって、不味（まず）いもん。
I also don't want to eat something like that. It’s because it tastes bad.
今日（きょう）は家（いえ）から出（で）ません。だって、今日（きょう）は暑（あつ）いもの。
I am not going to leave my house today. Cause it is hot today.