First, Jesus is speaking directly to his disciples. The Greek word ἀδελφός (adelphos) is being translated to "brothers and sisters" - as though Jesus is speaking in general to everyone.
This word means "brother - of the same parents" according to the lexicon, but also "a fellow believer, united to another by the bond of affection." Jesus is in fact addressing his disciples and students here - he is speaking and referring to his followers.
And he is speaking of how his followers should treat each other and help each other.
For example, Jesus isn't speaking of anyone going around and "rebuking" - or admonishing strangers for their sins. It is none of our business. This might be what fanatics like to do, but Jesus is not a fanatic. He is very practical.
Jesus wants his followers to help each other
Jesus wanted his students to assist each other in their spiritual growth. He wanted them to help each other, but also be forgiving of each other.
This misunderstanding of the intended audience of Jesus' statement here has led to ecclesiastical translators adding in words to make it sound more feasible. This includes the NIV translation here, where the translators have added the words "against you" to their translation - as though Jesus is speaking to everyone and speaking about someone sinning against us. There are no Greek words indicating "against us" in the original Greek manuscripts.
How can someone sin against us?
The word "sin" here is translated from the Greek word ἁμαρτάνω (hamartanō) - which means, "to err" or "to miss the mark." But when the context is one's relationship with God, the word specifically means, "to miss or wander from the path of uprightness and honor, to do or go wrong" according to Strong's lexicon.
Thus we find that the word relates specifically to wandering from one's spiritual path - more to the point - to wander from one's relationship with God.
This has nothing to do with how a person acts towards us. Jesus is not speaking of everyone being sensitive to how others "sin against" them.
He is speaking of his students helping each other - and forgiving each other - for their 'wandering' ways.
Surely a fellow disciple will admonish his fellow disciple or follower of his teacher when he sees them "wandering" from their path to God. He wants him to succeed in his journey home to the Supreme Being. But at the same time, according to Jesus, that fellow disciple should be immediately ready to forgive others' spiritual errors: Over and over again if needed.
This brings up the notion of forgiveness.
Does forgiveness necessarily mean that forgiveness excuses the responsibility - the consequence - of the action? Does having forgiveness cleansed or purified the consequence? Possibly. Or possibly not - depending upon who is doing the forgiving.
Let's give an example. Let's say that some high school bully emails out an embarrassing picture of a classmate to everyone in the class. This would be a pretty insulting thing to do, right? And we could admonish the classmate for doing that, right? It doesn't have to happen to us for us to be upset, in other words.
But then let's say that the bully becomes sorry, and expresses that he is sorry. Even though we weren't the person whose picture was sent out, we could still have forgiveness for the bully, right? But our forgiveness doesn't necessarily eliminate the consequence created by the act. The bully might be punished by a principal or someone else, even though we forgave them for doing that.
But if the bully expressly apologized to the classmate that had their photo sent out, and the classmate forgave them and decided not to report it, then those consequences could be mitigated - at least to some extent - by the victim.
Do you understand? A person who is not the victim of the insult can still be upset or forgiving. It is not necessarily the forgiveness that is necessary, however. In this example, we might tell the apologetic bully that he will need to apologize to the one he bullied.
In the same way, if we offend God by wandering from His path - and forgetting Him - then ultimately we need to seek forgiveness from God.
But this is why it is important that we associate with those who are trying to progress in their spiritual lives. Because we can help each other - by encouraging each other to stay on the path towards achieving love for the Supreme Being. This encouragement includes admonishment if we are wandering off the path - as well as forgiveness if we are feeling sorry.
Meaning of 'repent'
And by the way, the Greek word translated to "repent" - μετανοέω (metanoeō) - actually refers to having a change of heart (or mind according to the lexicon). It doesn't just mean feeling sorry. It means deciding to make changes in one's life, and in this case, it refers to a person deciding they want to return to our loving service relationship with the Supreme Being.
After all, this was the stated goal Jesus asked his students to attain:
“ ‘Love the Lord your God with all your heart and with all your soul and with all your strength and with all your mind’; and, ‘Love your neighbor as yourself.’” (Luke 10:27)