Is he considered an infidel, the one who likened himself to a Jew in harshness when he struck his children, based on his rejection of relying on custom for the meaning of the word, and his stipulation that the word "Jew" must appear with the meaning of harshness in Islamic law?

The ruling of disbelief on specific individuals is a judicial matter that falls within the purview of a judge, when the conditions are met and impediments are absent, due to the consequences that result from such a ruling. The statement by the person in question, "I do not attribute myself to the Jewish faith; rather, I meant that I am harsh when I hit my children," is an eloquent simile from which the instrument of comparison and the aspect of comparison have been omitted. This is common in religious texts and in people's speech. Contextual indicators (Qara'in) and common practice (Urf) are considered in Sharia (definition). Contextual indicators provide certainty, and common practice is a principle of legal deduction. One of the jurisprudential maxims is that "custom is given consideration." This is supported by the Almighty's saying: (Hold to forgiveness, command what is customary) and the Prophet's (peace be upon him) statement to Hind: "Take from his property what suffices you and your child in a reasonable manner." Therefore, these matters should not be nullified or ignored, especially in serious issues that result in excommunicating a Muslim from his religion.