Most of the seven deadly sins are defined by Dante Alighieri (c. 1264–1321) as perverse or corrupt versions of love; lust, gluttony, and greed are all excessive or disordered love of good things; and wrath, envy, and pride are perverted love directed toward others’ harm. The sole exception is sloth, which is a deficiency of love. In the seven deadly sins are seven ways of eternal death. Pride is often thought to be the father and promoter of all the other sins.

— Seven deadly sins, Wikipedia

I’ve heard about this often enough, but not how they are all related to love.

• perverse love of good things: lust, gluttony, greed
• perverse love for others’ harm: wrath, envy, pride
• deficiency of love: sloth

The love for other’s harm is relatively clearly Tolstoy’s law of violence.

Love of good things is perhaps a health issue? They’re seen as the ‘lower levels of hell’, a bit of lust never did me any harm, nudge nudge, wink wink.

Deficiency of love isn’t really a sin, just a shame. At least a sloth won’t do as much damage when infected by wrath, envy and pride.