This is why you're not justified in being so angry.

[frostmagemari]

No. In most cases it is quite literally my 2 "sense". How could you possibly think it meant anything otherwise?

"My two cents" (2¢) and its longer version "put my two cents in" is a United States (US) idiomatic expression,[1] taken from the original English idiom expression: to put in "my two pennies worth" or "my two-penn'orth." It is used to preface the tentative stating of one’s opinion. By deprecating the opinion to follow – suggesting its value is only two cents, a very small amount – the user of the phrase hopes to lessen the impact of a possibly contentious statement, showing politeness and humility. However, it is also sometimes used with irony when expressing a strongly felt opinion. The phrase is also used out of habit to preface uncontentious opinions.

The phrase "If you don't put your two cents in, how can you get change?" encourages an expression of opinion. It makes a pun on the word "change". One meaning of change is an alteration – presumably to bring someone or something in agreement with an expressed opinion. Another meaning of change is the cash equivalent of an overpayment. Thus the reference to two cents is in accord with another idiom that values opinions at one cent (penny for your thoughts).

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If you're going to use an idiom, use them correctly.