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Onions and garlic are dangerous if birds too eat much of it. A little bit won't hurt them, but should be avoided whenever possible.
Onions and garlic are part of the lily family of plants (includes chives, shallots, etc.) contain sulfur compounds that when metabolized can break down red blood cells (dipropenyl disulfide in particular). This can lead to diseases such as anemia.
It is worth noting that this affects humans too and some researchers theorize that the effect is less on birds than for mammals.
As it goes with most things related to nutrition (bird, human, or otherwise), a little bit isn't a big deal, but too much will kill you!