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Some people might not "get" the LOTH because on any given day, the psalter does not express their feelings, e.g. psalms of sorrow when all is well with their worlds, or joyful psalms when they are in the midst of suffering. But it's precisely a virtue of liturgical prayer that it breaks us out of the narrow confines of our own feelings and makes us think and pray as members of the Body of Christ. No matter what we happen to feel on any given day, we are supposed to pray the psalms in the voice of the Church on behalf of its members. There are always suffering souls to pray for, and there are always happy souls with whom we can rejoice. So we have to get over ourselves and pray with the heart of the Church; with the heart of Christ.
But once we submit to this discipline, a funny thing happens. We start finding a verse here and an antiphon there that jumps out at us so forcefully that it seems to have appeared in the day's Office as a "sign" or a message addressed to us by the Lord. And why not? Even as we pray on behalf of the Church for the world, we are also among the little sheep for whom the Church is praying.
So although it might be vain to expect each day's psalms to reflect our moods and needs, it's not vain at all to find elements in them that are deeply applicable to our personal situation.
God's Word will do that to you.