Why did Jesus ask His disciples to forgive the debt of their debtors (if they want their debt to be forgiven), if Jesus's atonement is universal?

The question gets to the root of historical Jesus studies in relation to Christian theology. Those who hold the the doctrine of the Bible's infallible verbal inspiration need to reconcile the two ideas mentioned in the OP. Those who accept that the NT writers present varied theologies rather than a unified doctrine answer more simply: Jesus taught something different from what the Church came to believe. These two schools of thought cut across denominational lines.

Paul's view

My answer is that Jesus actually taught something different from Paul, in particular. For Paul, God's forgiveness comes only by repentance and faith in Jesus' atoning death on the cross. In the end it is completely up to God, not man's efforts.

For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” It does not, therefore, depend on human desire or effort, but on God’s mercy. (Romans 9:15-17)

Some Christians will argue that Jesus did not mean literally what he said in the OP -- it really refers to what Christians naturally do after they are saved. Those who are born of the Spirit, as a matter of course, forgive each other's trespasses and love their enemies. This is based, for example, on Paul's teaching in Gal. 5:

The fruit of the Spirit is love, joy, peace, forbearance, kindness, goodness, faithfulness, gentleness and self-control... Those who belong to Christ Jesus have crucified the flesh with its passions and desires.

Jesus' teaching

However, it seems that for Jesus, one must indeed forgive others in order to be forgiven by God, not that one will forgive others IF one is saved and thus forgiven himself. That is the plain sense of the text in the OP. Indeed, the entire Sermon on the Mount may be seen as a teaching that one must act righteously to receive God's blessings, not that one WILL act righteously after one receives God's mercy. Jesus presents a list of commandments that go even beyond those of Moses, beginning with:

"I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven." (Mt. 5:20)

Later he concludes:

You have heard that it was said, ‘Love your neighbor and hate your enemy.’ But I tell you, love your enemies and pray for those who persecute you, that you may be children of your Father in heaven... Be perfect, therefore, as your heavenly Father is perfect."

The idea that one must do good deeds (such as forgiving others' trespasses) in order to be forgiven by God stands in tension with the idea that divine forgiveness depends entirely on God's predestination and one's faith in Jesus' atoning sacrifice. One way to resolve this tension is to explain that Jesus was actually talking about what Paul referred to as manifesting the "fruits of the spirit." But it must also be considered that Jesus actually taught that one must forgive others to be forgiven by God, not that one would naturally do so after being saved. In my view, the teaching of Jesus and the doctrine of Paul on this matter are simply different from one another

There are two different forms of forgiveness here.

When people forgive, they must discard any resentment or other negative feelings that they might hold against the former debtor.
When Jesus forgives, he never had any negative feelings for them in the first place, only love.

When people forgive, it relieves the sinner of a small obligation.
That is nothing compared with the result of Jesus's forgiveness.

Whether people forgive or not doesn't greatly affect the sinner, and certainly not in terms of salvation.
Jesus wants people to forgive completely for their own benefit, not for the sinner's.
Someone that harbours resentment etc. is not living as Jesus did, yet following his perfect example should be the goal of every Christian.

For more details, see my answer to Why does the Lord's Prayer instruct us to ask God to forgive us "as we forgive others"?

The doctrine of justification is not conditional upon our ability to forgive others. If so, salvation or justification in the eyes of God would not be a free gift.

13 In Him, you also, after listening to the message of truth, the gospel of your salvation—having also believed, you were sealed in Him with the Holy Spirit of promise Eph 1:13-14

Note nothing about forgiving others is mentioned here. Justification in the eyes of God or atonement for all sins past, present and future is applied as a free gift the moment one believes in Jesus.

Now that one is saved, they are to walk like Jesus walked. As you may know, this is a challenge for believers as they are a new spirit filled creation that lives in the same body of flesh that has desires contrary to God's desires. This is known biblically as the "flesh". There are consequences for believers including loss of eternal reward, and untimely death, etc that are results from believers not following Jesus. None of these is loss of salvation.

To that point I cannot conclude that our "forgiving others" is a condition for justification or maintaining our salvation. What are the consequences of a believer who is atoned for past present and future not forgiving another and thus not being forgiven by God? Loss of fellowship, loss of intimacy, bad example, loss of reward, bad example to others?

Example: If I do something to upset my wife and she doesn't forgive me that does not mean we are no longer married. That means that are fellowship and intimacy if broken. We may be miserable until we work things out or even die without ever working it out in this life. This does not invalidate the marriage. "I will not forgive you" does not have to mean "I take back the promise and Spirit I've given you"

Framing the question

I am providing an answer that I think all denominations agree on. Furthermore, I'm answering from the point of view of a disciple, defined as those who already declare Jesus to be their Lord and Savior. Within this limited context, we do not have to go into the dispute

• between inclusivism/exclusivism vs. universalism, or
• between limited atonmenet vs. unlimited atonement, or
• between perseverance of the saints ("once saved, always saved") vs. conditional security

because by definition a disciple is one who already receives Jesus's forgiveness from the cross by faith when he/she repented and converted to become son/daughter of God, and I want to provide an answer that is acceptable to both the "once saved always saved" group as well as the "we can lose our salvation" group.

So the question becomes: if we are already forgiven when we became a disciple, why does Jesus seem to condition our own forgiveness on our forgiving others?

Contextualizing the Lord's prayer and the forgiving command

In Matthew, the Lord's prayer is presented as a simple and trusting prayer model (as opposed to wordy / pretentious / vacuous prayers practiced by non-believers, cf Matt 6:5-8) containing essential daily requests that affirm our dependence on God in several areas:

• as children of God ("Our Father")
• citizen in God's kingdom ("Thy kingdom come")
• obedient to His will ("Thy will be done")
• a creature ("our daily bread")
• needing continual forgiveness from sins committed since we became Christians ("forgive us our sins")
• needing protection from evil ("deliver us from evil")

The bigger context is the Sermon on the Mount (Matt 5-7) where Jesus was emphatic that forgiving others (even enemies) IS the primary characteristic of the children of God (cf Matt 5:45), mentioning it in multiple places / contexts (even in the parables), not just in the Lord's prayer. For example:

• Reconcile before we worship God, Matt 5:23-24
• Do not retaliate even if they are wrong, Matt 5:38-42 following Jesus's example of forgiving enemies from the cross
• Love our enemies, Matt 5:43-48

We can see how Jesus's command in the Lord's prayer as the climax of his teaching on forgiveness, which he even repeats immediately after the Lord's prayer in vv. 14-15:

If you forgive those who sin against you, your heavenly Father will forgive you. But if you refuse to forgive others, your Father will not forgive your sins.

The answer

An acceptable answer by all denominations will be something like the following.

Disciples need to work out their salvation with the help of the Holy Spirit already given to them to become more and more like Christ. Therefore, we need to forgive others like Christ did his enemies, to do to others as Jesus has done to us. If our faith is genuine, we will do this, but in the weakness of our nature we need a constant reminder (thus included in the daily Lord's prayer).

Jesus's one time forgiveness on the cross needs to be realized in our consciousness and the way to do this is to realize how we are forgiven during the specific occasions when we forgive others by being Jesus to them because our sins to God are of various types and we need to realize how we have offended God and grieved others in multiple ways. By forgiving the various sins of others done against us we will then internalize instantiations of Jesus's forgiveness to us. For example, when we forgive other's unjustified anger to us, we are reminded that we need to be forgiven of our own anger. When we forgive other's betrayal, we are reminded how we have disappointed others too and need to be forgiven.

Another way to see this is that Jesus's death on the cross is a one time event of forgiveness (already received at conversion) waiting to be applied to a disciple's past, present, and future sins. Even a Calvinist who believes in TULIP cannot be certain if he/she is one of the elect. One way to have assurance is to observe his/her heart and see other's sin as playing itself out in him/herself saying:

"Looking at the root of other's sin, there may lurk in my heart similar propensity to sin that I either have done in the past or can potentially do in the future. As I forgive this person's sin against me today, I'm also applying Jesus's one time forgiveness to my particular sin as well and pray to God who is outside time to forgive me and heal me of this propensity".

If we do not do this, our faith may not be genuine, and let these refusal-to-forgive occasions come as a REALITY CHECK of our true relationship to God as children of God (a child of God would be ready to forgive). Thus, Jesus's teaching in Matt 6:14-15 can be seen as a gracious warning to help us make sure we don't deceive ourselves.