There are a number of reasons why carrots might be small. They can be affected by the soil composition and/or moisture content in the root zone, or they can have a genetic defect that causes them to not produce as much of an edible part of the carrot. In addition, carrots can be affected by how well the roots are grown (i.e. if they are grown on a flat surface or in the ground).
Carrots grown in the ground will have less surface area for air to circulate around them and may not get enough sunlight to make good sized carrots. Carrots grown in the ground can also be more prone to diseases and pests. The carrots may not have enough space to grow and therefore may not get as tall as they would if they were grown in pots or raised beds. The soil composition and/or moisture content of the root zone can also affect the size of your carrots. If the soil is sandy, the roots will not be able to absorb water as well. This can cause the roots to become dry and weak. If the soil is too wet, the roots will rot and die. If the soil is too compacted, it can make it difficult for roots to grow deep enough to get good sized carrots.