Why should we trust the writings of Paul?

We should trust any writings, by anyone, only when we understand them well enough to see that they got it right. Anything else boils down to treating written words as some sort of magical formulae. (That's were the word "grammarye," meaning magic, came from.) 

If you don't understand them that well, then it doesn't matter whether you trust Paul, because you can't trust your own understanding of the writings.

Paul's being chose by God should be enough to convince you.  And his writings show that they were God-inspired.

Of course, St. JOHN and his disciples all acknowledged St. Paul's writing, stating they were INSPIRED.

Good question, since Paul seems to have appointed himself apostle, and the only reason his letters are considered scripture is because his followers eventually took over control of the church.

You probably should not; Paul's writings contradicted the sayings and actions of Jesus. He was creating his own religion. Read the New Testament carefully and it becomes obvious.

Because his letters are also inspired by God.

Same reason we trust the rest of the Bible. The Holy Spirit guided the bishops of the Catholic Church when they compiled the Bible in the 4'th Century, at the direction of the Pope, to include only what God wanted included. If you don't accept that fact, there is no point in reading the Bible at all. If you do accept that fact, then you know that these 73 texts are the inspired Word of God.

All of the apostles got together 100 years after they all had died, and wrote the bible.  Otherwise, there is no way that they could get statements from all of them.

Of course they are God inspired and consistant with the rest of the bible....are you gay and looking for an out?

He was Gods own chosen apostle to bring the believing Jews and Gentiles together in the church.

Acts 9:15 KJV — The Lord said unto him, Go thy way: for Paul is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel.

1 Corinthians 1:17 KJV — For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.

2 Corinthians 4:5 KJV — For we preach not ourselves, but Christ Jesus the Lord; and ourselves your servants for Jesus' sake.

Colossians 1:28 KJV — Whom we preach, warning every man, and teaching every man in all wisdom; that we may present every man perfect in Christ Jesus: