I had a friend in the exact same situation. She was with her guy for around 10 years, they had one child and he wouldn't marry her. He'd tell her that he didn't believe in religion and religious ceremonies, that they didn't need to marry and to prove their love, that weddings were too expensive...money could be better spent on other things, etc.
They ended up parting the ways and a year later he married some other woman. The wedding took place in some lavish castle in the countryside. which would have cost a fortune!! Funny how the money had been worth it on this occasion.