An unbeliever can’t please God:

An unbeliever cannot come to faith by their own works because a person without faith can not do anything that pleases God. Our faith must precede any work that can please Heavenly Father.

Hebrews 11:6a:  But without faith it is impossible to please him

Man can’t work the miracle of faith:

The gift of faith is bestowed miraculously by the Holy Spirit; not by man.

1 Corinthians 12:3:  Wherefore I give you to understand, that no man speaking by the Spirit of God calleth Jesus accursed: and that no man can say that Jesus is the Lord, but by the Holy Ghost

It can’t be a work because God’s Word says we are not saved by works:

2 Timothy 1:9:  Who hath saved us, and called us with an holy calling, not according to our works, but according to his own purpose and grace, which was given us in Christ Jesus before the world began

Titus 3:5:  Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost; 

See also Romans 3:24-28, Romans 4:6-8 and Ephesians 2:8-9.

Conclusion:

“Faith is a work” is a logical argument. It holds no water when the light of God’s words is shown on it. From God’s word we gain understanding: faith is a gift, not a work.