Answer:
Because plants have many more stem cells, not only at meristems, regions of growth where unspecialised cells are actively dividing, but all through the plant. Adult cells easily revert to stem cells in plant culture, so a very small explant can be encouraged in agar medium to start to grow into a callus (undifferentiated ball of plant cells). We have learnt what combination of mineral ions and Plant Growth Regulators have to be added to the nutrient agar to make the transplanted callus start to develop roots, shoots and leaves.
Animals have fewer adult stem cells, and when fully differentiated, are more difficult to revert back to stem cells. Few of them will actively divide in culture, in vitro.