While watching a TV show , somebody had given a gift to a person, and then after certain unfortunate things that happened between them, the giver decided to keep the gift, somebody else tried to convince the giver to give the gift back, the giver didn't want to, and he was told, that's called " indian giving" , somebody mentioned that that was a very racist term , is it a racist term ?
Does "Indian Giving" always mean that somebody is gonna keep something that was given as a gift ?

Sorry, but yes it does mean that they may give you a gift, but they'll ask for it back later. And, of course, people that used this expression were considered racist, because they insinuated that Indians did not have good moral standards or understand what it meant to give someone a gift. It probably also insinuated that they may give you a gift, but may even steal it back, since many whites were very prejudiced when this term was coined.
You can be the judge, Qtivan:

'Q: What is the origin of the phrase "Indian giver"? When did it come about? Did it always imply that the giver was duplicitous? I can think of several alternate original meanings. For example, it could have been a white description of native North American potlatch ritualistic giving and receiving (albeit misunderstood), and in this sense, an evaluatively neutral description. Or, it could have been a pejorative referring to whites' practices of "giving" something to the Indians and then taking it back when the land became needed. Or, it could reflect and essentially neutral description of the whites' interpretation of native's unfamiliarity with the conventions of bourgeois private property, as imported from Europe and imposed on this continent. -- Dan Poor, New York City.'

A: Surveying the various explanations for "Indian giver" you offer, I'd say the truth contains a bit of all three. The phrase dates back to the early 19th century and originally meant someone who gives a gift in the expectation of receiving something of greater value in return, which was indeed a custom among Indians that must have struck early European settlers as rather odd. Later on, the phrase came to mean a "false gift," as the adjective "Indian" itself took on the pejorative meaning of "false" or "mock," a sense also found in "Indian Summer" and "Indian corn." While it's true that the European settlers had a far worse reputation when it came to trustworthiness than the Indians did, the victors in history usually get to make up the idioms, so it's doubtful that "Indian giver" refers to the manner in which the settlers treated the Indians. It would be a quite a stretch to credit 19th century European settlers with the honesty to have recognized that they, and not the Indians, were the "Indian givers" in most cases. '

But, yes-- it always means giving a gift and then asking for its return.
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i have had a first nation fellow in canada explain to me that in the historical traditions of his culture, if a gift was givin for a reason, and never utilised for such, it could be taken back to give it to another who would use it..... imagine i gave you a lawn mower so you could keep your grass under control, if you did not use it at all, i would be inclined to take it back and give it to someone else who needs one.... it is based on the understanding that the world has finite resources, and they should be used appropriately, not squandered,,, for the reason just to have...
No. I do not think so. First of all, it is not Indian tradition to give gifts, even in their first visit. It is Japanese culture and style. However, if someone gives the gift in first meeting, it is usually kept with the host. he accepts that.
Anonymous: in this expression 'Indian' refers to Native American people / first nation people not people from the Indian subcontinent. Gift-giving, by the way, is a tradition in many cultures, not just in Japan.
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 indian giving refers to the belief in reciprocity common among many Native American groups; when one gives a gift, it is expected that the receiver of the gift, at some point in the future, reciprocates by giving a gift of equal or greater value to the individual who first gave the gift.
Europeans didn't understand the concept, and didn't understand why an Indian individual or group felt entitled to a gift after they had themselves had given one previously.