*חלבי ודמי הנמעט בצומי

For Ta’anis Bechorim ,a father or mother is required to fast for their child who is under Bar Mitzvah even if the child hasn’t reached the age of Chinuch. 
 No other Ta’aneisim is the parent required to fast for their child. Ta’anis Bechorim is different than the other Fast days. Fasting on the other days is a Mitzvah. 

Only Gedolim are Mechuyav to perform Mitzvohs. 

 Fasting Ta’anis Bechorim is for protection of the Bechor. All Bechorim regardless of age, need the protection. The first nine Makos didn’t need a special protection for the Bnei Yisroel. It was sent specifically,to the Mitzrim. 

Makas Bechoros was different. It was sent down to all inhabitants of Mitzrayim,Yidden & Mitzrim. For the Yidden not to die, they required Dam Pesach & Dam Milah. They also, weren’t allowed to leave the house. The Bechorim needed this special protection from the Makah. Chazal instituted Ta’anis Bechorim to commemorate the special protection that was needed, to save the Bechorim in Mitzrayim with the Dam Hanimat B'tzom *Selicha Yom Kippur Koton 

(Masas Chapai-R. Mordechai b. Shabsi Aruch)