How refreshing, an actually reasonable point about faith.
I can provide a response but this one is going to require some in depth information.
To start with passages like these are where that belief comes from:
New International Version
"Why does this fellow talk like that? He's blaspheming! Who can forgive sins but God alone?"
New International Version
Who is a God like you, who pardons sin and forgives the transgression of the remnant of his inheritance? You do not stay angry forever but delight to show mercy.
New Living Translation
"I--yes, I alone--will blot out your sins for my own sake and will never think of them again.
A Psalm of David.
1Bless the LORD, O my soul,
And all that is within me,
bless His holy name.
2Bless the LORD, O my soul,
And forget none of His benefits;
3Who pardons all your iniquities,
Who heals all your diseases;
4Who redeems your life from the pit,
Who crowns you with loving kindness and compassion;
5Who satisfies your years with good things,
So that your youth is renewed like the eagle.
6The LORD performs righteous deeds
And judgments for all who are oppressed.
Psalm 103 NASB
It is a given that the bible claims that only God can forgive sins but as you pointed out in a few places it commands us to forgive. We can really get into this issue by looking up the original Hebrew, Aramaic, and Koine Greek that the verses were originally written in so as to eliminate problems with interpretations and we can get into the great commentaries on these issues but first let me state what I believe we will find if you wish to dig deeper.
I believe there is a virtually infinite difference between what we forgive and what God forgives. We merely cease holding another's sins against us when we forgive but we cannot wipe out the actual eternal sin debt a person has before God. No matter who and how much we forgive that person will still be guilty and condemned before God for the sins we stop holding against another. Only God can clear the actual debt that sin incurs, we can merely provide relief from vengeance against others who sin against us. How is that? Can we agree on that or do you want to go deeper into this?