Have you ever noticed just how much of the fruit of the Spirit exists for our relationships? Love is for others, as is peace, patience, kindness, goodness, faithfulness, and gentleness. Joy and self-control are primary for us, but can also be quite useful towards others.
Galatians 5 teaches us that when we walk by the Spirit, He will produce His fruit in us. Many of us measure our success at walking by the Spirit with how much joy and self-control we have, the two inward fruits. But I suggest that the real measurement of whether we're walking by the Spirit should be how we're interacting with others! It's easy to be a peaceful monk in the garden when no one else is around. What kinds of fruit are growing out of you when you're dealing with coworkers, neighbors, family, and fellow church members?
Galatians goes on to say, "Now those who belong to Christ Jesus crucified the flesh with its passions and desires." Which of your passions and desires are bringing the strife into your relationships? Your desire to be heard instead of listening? Your desire to be thought of more highly? Your desire to be served rather than to serve? Think of all the people who have switched churches to find one that "caters to them". Think of all the spouses who have walked out of their marriages because they weren't "in love" anymore. This behavior comes from self-centered desires that should have been crucified with the flesh a long time ago.
Walking by the Spirit doesn't just mean achieving a measure of inner peace. It really means crucifying the flesh, eliminating the passions and desires which stand in the way of living in a godly manner towards Christ and others.