Jesus uses the ideal of forgiveness to expose sin
Jesus came to "fulfill" the law in the sense of idealizing it. He does this to remove any claim to a righteousness gained through obedience. His teaching on forgiveness sometimes serves this purpose. He makes it clear that since God is willing to forgive our sins, we are bound to forgive those who sin against us. He warns that a failure to forgive will undermine any claim to a right standing in God's sight. So, Jesus demanded perfect forgiveness of the apostles. His purpose was to remind them that their standing in the sight of God, the maintaining and progressing of that standing, remains a gift of grace through faith. Yet, who can claim to forgive as God forgives?
Sadly, the pietist today seems able to ignore the obvious and claim an ability to forgive. We do this by either reducing the law's demand (eg. we only have to forgive those we judge are Christians.....), or denying our imperfection by concentrating on the imperfection of others.
Jesus uses the ideal of forgiveness in much the same way as he uses other ideals of the moral laws. For example, with revenge, Jesus demands an ideal of turning the other cheek, Matt.5:38-42. This is an impossible ideal in a sinful world. Of course, so is "forgive people when they sin against you", Matt.6:15,16. Obviously the "righteousness that surpasses that of the Pharisees and the teachers of the law", a righteousness which we must reach if we are to "enter the kingdom of heaven", will have to be gained by means other than obedience, Matt.5:19,20.
The parable of the Unmerciful Servant is an excellent example of this particular use of moral ideals, Matt.18:21-35. Although the Pharisees taught that a child of God was to forgive a brother three times, Peter was willing to try seven times. Jesus demanded seven times seven (probably seventy times seven). The ideal is to always "forgive your brother from your heart". Note the context of this passage. Jesus follows up this ideal with the ideal on divorce, but then goes on to remind us that the kingdom belongs to little children who come to him, Matt.19:13-15. Then follows the story of the rich young man who is reminded that "eternal life" is not gained by obedience. "With people this is impossible, but with God all things are possible." Hopefully Peter got the message. Such righteousness cannot be done, only given.
So, "forgive and you will be forgiven" serves to place us firmly at the foot of the cross. Jesus uses this ideal to remind us that our failure to obey places us under a curse and that therefore righteousness can only be gained as a gift of God's grace through faith apart from works of the law.
Jesus uses the ideal of forgiveness to shape our Christian walk
When it comes to righteousness in the sight of God, we are bound to rest on Jesus' perfect obedience and so share in his blessing. He is the only person who could forgive his brother seventy times seven, love his enemies and do good to those who hate him, Lk.6:27-36.
Yet, this doesn't mean that we can ignore the ideal of forgiveness. Moral ideals are not to be ignored, but rather pressed at. Therefore, "bear with each other and forgive whatever grievances you may have against one another. Forgive as the Lord forgave you", Col.3:13. Aim at perfection, but remember, "there is no perfect Christian", Luther.
Forgiveness is a natural response for those who walk by the Spirit
There are those who are righteous through faith and there are those who are righteous through works (a faithful attention to the law). The righteous through works simply don't realize they are sick and in need of a physician, Lk.5:31-32. They deny their sin and hide their guilt in a judgmental spirit, Lk.18:9-14. The righteous through faith know they are sick and in need of a physician. They admit their sin and find in Christ the source of forgiveness.
Forgiveness is a quality naturally found in a forgiven person. It is not perfectly evident in a believer's life, but when we hear Jesus' call us to forgiveness, we move in that direction. The more we are forgiven, the more we forgive, Lk.7:36-50. When we walk by the Spirit, daily renewed by him, or if you like, when we walk hand-in-hand with Jesus through life's journey, we will find ourselves better able to accept the failings of others, better able to welcome into our fellowship the fallen and damaged refuse of society, and this because God in Christ welcomes us. The forgiven tend to forgive.
So, when Jesus' calls on his followers to display a forgiving nature, he is asking for a reasonable and natural response which has the support of the indwelling Spirit of Christ. A person possessed of a judgmental spirit has likely drifted from the mercy of God in Christ and needs to place themselves again at the foot of the cross.
There can be no forgiveness without repentance
Many believers think they are required to practice a level of forgiveness greater than God. God only forgives those who repent, but we are often castigated from the pulpit if we don't forgive everyone who harms us, and do so even if their harassment is repeated. Many believers are psychologically affected by a belief that they must be accepting of the most nasty individuals. Many Christian women put up with both physical and mental harassment from abusive partners, all because they believe it is Christ's will for them. Yet, the truth is, it is not God's will that we be a door-mat.
Nor is it healthy to go to the opposite extreme. We don't have to be twisted with anger and bitterness just because someone hasn't said sorry. We should follow the approach of the psalmists who simply handed their enemy over to God to vindicate their cause. We do well when we disengage and hand the person over to the Lord for his mercy.
The Lord does not ask us to practice a form of forgiveness that outshines his own, Lk.17:3.
What Christ asks we can do, by grace through faith
As a young minister, I found myself in a conflict with an elderly lady in our church. The situation was really quite out of hand and there was certainly no mercy, no forgiveness between us.
One Sunday morning during the communion service, feeling totally defeated, I simply said to the Lord, "this situation is beyond me, please help us grow in love." And he did! Both of us came out of the service that Sunday, totally bound to each other in love. Forgiveness for each other was total and remained so. From then on she was my mother in the Lord, and I was her son. Quite unbelievable!
I am sorry to say, this was a rare and special miracle. There are still a few brothers and sisters out there who I am quite happy never to meet again. Still, the experience reminded me that in the power of the indwelling Spirit of Christ, we are able (at times) to forgive as Christ forgives.
Paul in 2Corinthians 5:14-15 encapsulates this truth. Christ's loving character indwelling us, "compels" us to "no longer live for [ourselves] but for him who died for" us. At times the Spirit transforms us, by grace through faith.
Forgiveness in the Lord's Prayer
Finally, we should take a moment to look at the link between our inability to "forgiven everyone who sins against us" and God's willingness to answer the prayer, "forgive us our sins", Lk.11:1-13.
It is most unlikely that Jesus is using his "moral-ideal" methodology in the Lord's prayer. That is, he is not trying to expose sin. Nor is he here guiding us in the Christian life. Nor is he suggesting that there actually is a link between our capacity to forgive and God's forgiveness of us. Such a line undermines the gospel.
We are most likely dealing with an idea often found in Jesus' teaching on prayer. It is the "how much more" line. If I can forgive sometimes, imagine the extent of God's forgiveness. The parable of the midnight guest makes this point, Lk.11:5-8. (Note, this parable is not teaching persistence in prayer). If a friend will answer my request with a bit of a push, imagine how much more God will answer my requests. If a father knows how to give good things to his son, imagine "how much more your Father in heaven" will give you when you ask him, Lk.11:11-13. (Note, as with most statements on prayer in the Bible, the "ask and you will receive" is not a blank cheque. Asking must always be "according to the will of God", 1Jn.5:14. Here God promises his Holy Spirit to those who ask. God gives what he has promised.)
So, the phrase on forgiveness in the Lord's Prayer reminds us that we are asking something of God that even we are able to do, although imperfectly. If we are sometimes able to forgive those who sin against us, imagine how much more God can forgive.
Jesus' demand for perfect obedience, perfect forgiveness, reminds us that we can only ever stand under his perfection. None-the-less, we are to strive toward a forgiving nature, we are to strive to be the person we are in Christ. For in the end, a capacity to forgive is a natural quality for a person washed by the grace of God's forgiveness.