The willingness to give up one’s life to sanctify the Divine Name stems naturally from the nature of the Jew, who cannot separate from God. If a Jew were conscious of how any sin separates him from God, he would never sin. It is the evil inclination that deceives a person into thinking that he will be able to sin yet still remain connected to God.

A Jew cannot be separate from God:

Part of the nature of the Jewish soul is that it cannot be separate from God – “For You are our Father” (Isaiah 63:16). Because of that, even the most frivolous people or the sinners of Israel give up their lives to sanctify the Divine Name. They will not worship idols, God forbid, even if gentiles take their lives away, for they are unable to separate themselves from the unique, one God, may He be blessed.

If a Jew sensed the import of every sin, he would give up his life rather than transgress:

If he knew that through a particular evil act he would become separated from God, there is no way he would do it. However, the evil inclination entices him to think that he will nevertheless not be separated from God and will remain like any other Jew who is faithful to God. It also assures him that things will be good for him as it is written: “He will bless himself in his heart, saying: Peace will be with me, as I will follow the desire of my heart” (Deuteronomy 29:18). Even if he follows the [sinful] desires of his heart, nevertheless peace will be with him. In this manner he transgresses in various ways. (Rabbi Shalom Dovber Schneersohn, Kuntres UMa’ayan 2:1)

Further reading: For more on the meaning of the words “with all your soul,” see A Concise Guide to the Sages, p. 232.