What makes the big toenail start to turn inward?

Many reasons: Usually it starts growing inward or deformed after some type of trauma to the nail. There also could be an underlying problem below the nail that causes it to do this. Fungus is a common reason for it.

Most common : Reason is not cutting nails straight across. If you curve the ends you will end up with ingrown nails.

Shoe pressure: Ill-fitted shoes, narrow shoes, high heels, improper nail trimming, history of nail injury/ toe injury, growing bone bump/ subungual exostosis - all could be the cause of the ingrown toe nails.