Ahhhh, whining. I worked in daycare and as a nanny for years and swore my kid wouldn't do it.
My DD#1 has this thing where she just goes, "eh-eh-eh-eh" and points ot what she wants. She does this and my parents, husband and MIL collide trying to get whatever it is she wants. I'm exaggerating (just a tiny bit) but they don't discourage her at all from whining. I always tell her, "I don't understand you when you whine" or "use your words like a big girl" and she'll try to say what she wants (she just started speaking 'english' this month...she has her own language where she'll say complete sentences to you and expect you to understand her even though they sound more like chinese. My brother's girlfriend is Chinese, though, and doesn't understand her so there goes that theory!!

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I tell them to make her say what she wants but they still give in.
I think as long as you stand your ground and don't give in, they learn not to whine. There are times, however, when they won't care. Examples are when they're hungry or tired. I have found that she is the worst when we she's starving. You CAN'T reason with them then.
My DD#1 also just learned, "no" this weekend. She never used the word before this weekend. She doesn't just say it, though, she WHINES it. "nnnnnnnoooooooo" makes me cringe just thinking about it. I don't think she fully understands what it means b/c she's using it even when she means yes. I use the same, "I don't understand you," but I think she likes to use the word. I'm hoping she will outgrow this.