What's the law when a father kills his kids?

The law on parricide applies when a father kills his children. For example, on Christmas Day of 2020, tragedy struck a family of four in Taguig City on Christmas day when the father hanged his two young children in their home after his wife, reportedly a call center agent, committed suicide on Christmas eve. (Jonathan Hicap, 2020. Pa kills two kids on Christmas Day after wife commits suicide. https://mb.com.ph/2020/12/25/pa-kills-two-kids-on-christmas-day-after-wife-commits-suicide)

Taguig City Police Chief Col. Celso Rodriguez identified the suspect as Aiko Siancunco, 29 of Kamias St., North Signal, Taguig City who hanged three-year-old Akira and Kion, 1 at about 7:30 a.m on Dec. 25. Rodriguez said prior to the incident, Siancunco’s wife Karina committed suicide in the afternoon of Dec. 24. Siancunco reportedly suffered depression because he is jobless that led to a rift with his father and siblings and also a cause of conflict with his wife who was supporting the family. After killing his kids, Siancunco reportedly tried to commit suicide by hanging himself and drinking bleach but the cord reportedly snapped. He later surrendered to the police. (Jonathan Hicap, 2020. Pa kills two kids on Christmas Day after wife commits suicide. https://mb.com.ph/2020/12/25/pa-kills-two-kids-on-christmas-day-after-wife-commits-suicide)

Parricide is the most terrible and unnatural of crimes. (Cassiodorus, The Letters of Cassiodorus) It is said that, in Romulus’ time, there was no penalty for parricide because it was considered a crime too evil ever to be committed. While parricide in those days referred to the murder of one’s own parent or ascendant, the killing of one’s own offspring, which the term’s modern meaning now includes, is equally horrendous and deserving of the stiffest penalty. (People v. Tibon, G.R. No. 188320, June 29, 2010

Article 246 of the Revised Penal Code (RPC) defines parricide as follows:
Any person who shall kill his father, mother, or child, whether legitimate or illegitimate, or any of his ascendants, or descendants, or his spouse, shall be guilty of parricide and shall be punished by the penalty of reclusion perpetua to death. (Emphasis supplied)
Parricide is committed when: (1) a person is killed; (2) the deceased is killed by the accused; (3) the deceased is the father, mother, or child, whether legitimate or illegitimate, or a legitimate other ascendant or other descendant, or the legitimate spouse of the accused. (People v. Castro, G.R. No. 172370, October 6, 2008)

Among the three requisites, the relationship between the offender and the victim is the most crucial. This relationship is what actually distinguishes the crime of parricide from homicide. In parricide involving spouses, the best proof of the relationship between the offender and victim is their marriage certificate. In parricide cases involving parents and children, the best proof of the relationship is the birth certificate of the latter. Oral evidence, however, may also be considered in proving the relationship between the two as long as such proof is not contested. (People v. Paycana, Jr., 574 Phil. 780)

Parricide is differentiated from murder and homicide by the relationship between the killer and his or her victim. Even without the attendant circumstances qualifying homicide to murder, the law punishes those found guilty of parricide with reclusion perpetua to death. The commission of parricide is punished more severely than homicide since human beings are expected to love and support those who are closest to them. The extreme response of killing someone of one’s own flesh and blood is indeed unnatural and tragic. Parents killing their children must, thus, be handed down the harshest penalty for such crimes against innocent children, their children. (G.R. No. 188320)

The mental state of Aiko Siancunco, however, is a determinative factual question that must be threshed out in court. Moreover, please note that the law on infanticide may chance the discussion above.