"If the Satan did not blind our eyes, we would all see that these children [in secular schools] are like the children on the trains to Auschwitz.” Saving a captured soul is the greatest mitzvah, especially today!
Simcha (happiness) from learning Torah and doing mitzvot can eliminate harsh degrees that were not nullified during the Days of Awe! Those who do not have this true happiness can fall into the hands of those who hate the Jewish people and wish to do them harm.
Personal holiness and personal protection – how can the former bring about the latter? The Kalever Rebbe explains that only through personal holiness can one live in Eretz Yisroel in peace and tranquility. It provides the merit to protect one from all enemies.
Your family needs to see how happy you are when you study Torah! If they see this joy, they will surely follow your example. However, if they see you focusing on other matters, it won't help to tell them to learn because you've shown them that you have different priorities in your life.