Where in the Bible does it say let each man believe his own day of worship?
It doesn't say, "let each man believe his own day of worship,"
however, it does talk about "esteeming" one day above another.
Romans 14:5,6
5 One man esteemeth one day above another: another esteemeth
every day alike. Let every man be fully persuaded in his own
mind.
6 He that regardeth the day, regardeth it unto the Lord; and he
that regardeth not the day, to the Lord he doth not regard it. He
that eateth, eateth to the Lord, for he giveth God thanks; and he
that eateth not, to the Lord he eateth not, and giveth God thanks.
(King James Version)