Why are rabbits allergic to carrots?

Rabbits are not allergic to carrots.

However, carrots are very high in sugar and if a rabbit indulges in too many sweets, various complications can result, all of them possibly leading to the rabbit's death.

A bite or two of carrot every couple of days will not harm your rabbit (assuming she's otherwise healthy and eating a healthy diet. See the related questions below for more info).

Carrot greens, on the other hand, are very healthy for your rabbit and you can offer them regularly!