A school of thought believes that asking God for forgiveness is a waste of time which makes me wonder why Jesus himself wasn't against asking for forgiveness when he taught on the Lord's Prayer (MATH 6: 12)


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When thanksgiving fills our hearts, it wouldn't just reflect in our prayer or from our lips; it should reflect in the way we live our lives.Thanksgiving should become natural in our relationship with God at all times, under all conditions, and in all circumstances. (1 thes 5: 18). Who says you can't engage in the prayer of forgiveness with the heart of thanksgiving?
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When it comes to prayer or relating with God, He is far more interested in our hearts than He is in our words. Remember God's testimony of Abraham without him physically sacrificing Isaac( GEN 22: 12), his testimony of Job despite his ignorance (JOB 42: 8), remember Cornelius didn't have to verbally confess Jesus as Lord before he was filled with the Holy ghost (ACT 10: 45,45). Repentance is an act that consciously or unconsciously seeks forgiveness; a noble act that attracts forgiveness; God's more interested in our attitude and heart than just words from our lips.
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You shouldn't feel comfortable when you fall into the mud. That uncomfortable feeling isn't because you're guilty/sin conscious. When God is your father, you shouldn't feel too big to tell him sorry. Apologizing not with a mindset of "it doesn't matter if I repeat it" but that of "I believe I can change through the work of your Spirit in me."
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We repent knowing that God is a forgiving and loving God who has provided a means of forgiveness in the sacrifice of His Son on the cross. We confess our sins because we know “He is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness” (1 John 1:9)