Because that's the way God wants us to do it. In James 5:16, God, through Sacred Scripture, commands us to "confess our sins to one another." Notice, Scripture does not say confess your sins straight to God and only to God...it says confess your sins to one another.
In Matthew, chapter 9, verse 6, Jesus tells us that He was given authority on earth to forgive sins. And then Scripture proceeds to tell us, in verse 8, that this authority was given to "men"...plural.
In John 20, verses 21-23, what is the 1st thing Jesus says to the gathered disciples on the night of His resurrection? "Jesus said to them, 'Peace be with you. As the Father has sent me, even so I send you.'" How did the Father send Jesus? Well, we just saw in Mt 9 that the Father sent Jesus with the authority on earth to forgive sins. Now, Jesus sends out His disciples as the Father has sent Him...so, what authority must Jesus be sending His disciples out with? The authority on earth to forgive sins. And, just in case they didn't get it, verses 22-23 say this, "And when He had said this, He breathed on them, and said to them, 'Receive the Holy Spirit. If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained.'"
Why would Jesus give the Apostles the power to forgive or to retain sins if He wasn't expecting folks to confess their sins to them? And how could they forgive or retain sins if no one was confessing their sins to them?
The Bible tells us to confess our sins to one another. It also tells us that God gave men the authority on Earth to forgive sins. Jesus sends out His disciples with the authority on earth to forgive sins. When Catholics confess our sins to a priest, we are simply following the plan laid down by Jesus Christ. He forgives sins through the priest...it is God's power, but He exercises that power through the ministry of the priest.