One way of solving problems in a marriage is turning away from them - and your partner - pretending and perpetuating the illusion that the problems don't exist. Another way of solving problems is turning away from your partner in anger and starting cold wars of no communication at all. The healthy way of solving problems is using healthy anger to turn toward your partner in a way that pushes both of you to an argument/discussion that's honest without being insulting or abusive. That recognizes that the partners have an equality that allows for honest anger.
Marriages today - like our society - are having great difficulty with the concept of power-sharing between husbands and wives. It's rare to see a marriage on television or in the movies in which both husband and wife are portrayed as strong, mature, and caring, a couple who share responsibilities and decision-making for themselves and their family. (One good example, so far, are the husband and wife in "Madame Secretary.")
Yet Scripture suggests that this is how God created us to be - equals. In the first Creation story we read "God created man in His image; in the divine image he created him; male and female he created him." (Genesis 1: 27.) If both man and woman are created in God's image, they represent God's Nature equally.
This is re-enforced later on: "The Lord God said "It is not good for the man to be alone. I will make a suitable partner for him." (Genesis 2:18.) "Partner" is a word we use to suggest two people working together - in equality.
God casting Adam into a deep sleep and forming woman from a rib God takes from Adam's side has been misused to suggest that woman belongs to man as a part of him that he has control over - an idea re-enforced by males being physically more powerful than females. So even in Scripture, in the Old Testament, you see men's sinfulness in treating women as their property. But the passage suggesting that woman is made from man's rib exists to symbolize oneness, not domination.
In the Gospels, Jesus (Who is God's Son) confers equality on women: when he visits the home of his dear friends Martha, Mary, and Lazarus, Mary is allowed to sit at his feet and learn in the posture of a disciple at the Master's feet, a remarkable non-sexist situation for a teacher to allow in first century Palestinian Judaism. The Risen Jesus sends Mary Magdalene to tell the apostles that he is indeed risen, which has led to Mary Magdalene being called "the Apostle to the Apostles."
In marriages today, there needs to be constant, honest communication to affirm the honest concerns and opinions of both husband and wife. Because in a marriage, as in society, there is either a tendency toward matriarchy (the woman in charge) or patriarchy (the man in charge), both have to work for a balance. To have a full, rich relationship, both need to work together as one, in a balance of power and authority, valuing both people's opinions, knowledge, and concerns.
Anger is an energy which is part of our defense system; it is meant to strengthen us to protect ourselves and/or defend ourselves. Anger does not have to be used to attack another - but to stand up for one's unique self. To explain where a person stands on a topic. To ask for respect.
An argument between a husband and wife, then, is not necessarily a bad thing. If both people love and respect each other, it is far better for negative thoughts and feelings that may have been held in to come pouring out and see the light of day. Only the truth can set an individual and a relationship free. Only the truth of one partner baring how he or she thinks and feels can empower the other to either say "I'm sorry" or "Now I understand" or "You are misunderstanding me."
A strong marriage, always searching for the truth, is strengthened by a torrent of honesty. A weak marriage will either begin a necessary disintegration in the face of truth, or a necessary re-integration and growth, because it was initially built on lies and illusions and deceptions rather than on an honest commitment by two mature, free people with God as their Partner.
A good, honest argument always needs to end in one way: "I love you." The things each one has said may have been painful for the other to hear. But now love has to be expressed and exchanged - in words, in kisses, in embraces, in making love - so the relationship can move forward and deepen and grow. So that MORE love can be made. Then both can say "This one is bone of my bone and flesh of my flesh." For - "Deep waters cannot quench love, nor floods sweep it away..." (Song of Songs 8:7.)
If God has brought you two together, pray together. Together ask God for the wisdom, the maturity, the love to always be transparent with one another. Then, if God has truly joined you into oneness, nothing can separate you!