Which pets are kosher to buy for a child?
Why cats are forbidden to take care of as a pet? Many times they are saving lives of their owners.
All pets are permitted, including cats — with the exception of dangerous animals.
One who owns pets must be careful to fulfill the relevant halachos, such as feeding the pets on time, treating them correctly on Shabbos, and so on.
A number of sources indicate that it is not worthy practice to have pets in general. These sources see in having pets “divrei hevel,” and consider the practice illegitimate. See Koheles Rabba Chap. 6, Aruch (aruch davar 2), and Sefer Chasidim (1038).
However, a number of halachic sources write that the practice is permitted. See Birkei Yosef (Yoreh De’ah 117) based on Beis Yosef concerning a parrot, and see Shut Yachin U-Boaz (Vol. 2, no. 25) concerning a monkey, and Kaf Ha-Chayim (Yoreh De’ah 117:5) concerning others birds.
Some object to pets because a person should dedicate his love and affection to others (humans), and not to animals. However, pets can be productive in the development of children, and this is a personal matter for your discretion.