To get the bear's paw, you must use the fish as bait. To get the fish, you must drive away the bear (lose the bear's paw). Therefore, you cannot have both the fish and the bear's paw.

The source of the saying "You can't have both the fish and the bear's paw" is:

Mengzi (孟子-告子上), the author of which is most likely Meng Zi (孟子).

Related text:

The fish is what I desire, the bear's paw is what I desire, and you can't have both, so you have to give up the fish and take the bear's paw. I want life, I want it, I want righteousness, I also want it. The two are inseparable, and the one who gives up life for righteousness is also the one who gives up life for righteousness.

Related translations:

Fish and bear's paw are both delicious and I want them both, but it is impossible to get them both, so I will take the bear's paw, and life and righteousness are both what I want, but if I can't get both, I would rather lose my life in order to fulfill righteousness.

The truth of the saying "you can't have both the fish and the bear's paw":

Meng Zi's words are a warning to people that they should emphasize righteousness, and would rather give up their lives than take the righteousness, but people tend to forget the original meaning of this saying, and are happy to talk about the fact that you can't have both the fish and the bear's paw. Although, this is also a truth. People can not be too greedy, things can not let a person take advantage of all the advantages, some gain must be some loss, we should learn to give up the secondary and care about the important.

"Fish and bear's paw can't have it both ways"

Meng Zi first used the concrete things that people know in life to make an analogy: fish is what I want to get, bear's paw is what I want to get, and I'd rather give up the fish than the bear's paw in the case of the two can't get at the same time; life is something that I cherish, and righteousness is something that I cherish, and in the case of the two can't get at the same time, I would rather give up the fish than the bear's paw; life is something I cherish, and righteousness is something I cherish. I cherish life, righteousness is also, in the case of the two can not be obtained at the same time, I would rather give up life and want righteousness.

Mengzi compares life to a fish and righteousness to a bear's paw, arguing that righteousness is more precious than life, just as a bear's paw is more precious than a fish, which naturally leads to the proposition of "sacrificing one's life for righteousness". This claim is the central argument of the whole article.