Is a son considered to be severing ties of kinship if he refrains from meeting his father after the father gave him a choice between him and his mother and siblings, while the son continues to send messages of congratulations and inquire about his health without receiving a reply?

Satisfying your parents, showing them piety, and treating them well are obligatory. Part of showing them piety is striving to reconcile them, although divorce can sometimes be more appropriate. You and your siblings should try to study the causes of the dispute and gently approach them so that they may come to their senses, as reconciling them helps to please them and carries a great reward. Your father should be made to understand, with wisdom, that there is no contradiction in showing piety to both parents, for each has a right, and neither should stipulate that pleasing them requires disrespecting and angering the other party. You must be keen to maintain contact with your father, exert effort in treating him well, and supplicate for him, and urge your siblings to do the same.