Three of swords in many ways may be on of the most riddling allegoric messages of Tarot. It is a teller of lover triangles, and often includes deceit, jealousy, and emotional agony.
Not every love triangle is in context of infidelity of course, there are many situations and lifestyles where people are accepted in having more than one partner. Though these triangles may be consented, some of the same issues and insecurities may appear.
The three of swords sits under the three of the Major Arcana, The Empress. The core value of the Empress is bounty, plentiful goodness, nurturing. It is to say that there are many beautiful things in the world, and you are never lacking. When we acknowledge that there is enough love to go around for all beings and you are worthy of it, you may be able to let go of attachments to relationships that do not serve you, and detach from rivalries that distract from being a whole person.
The swords of each card in its suit have slippery blades, even when mastered as a tool to further the capacities of our hearts, some lessons may be cutting. We are allowed to keep going, to learn and grow fearlessly into people of integrity and light. Nothing can keep us down.