Many people write Teacher's Day as Teacher's Day. In fact, Teacher's Day is wrong. Teacher's Day refers to all teachers' holidays, not one teacher's holiday, so S comes first.

In English, when mentioning names, places, countries, festivals, weeks and months, the first letter should be capitalized.

For example: Monday, September, China, Beijing, etc.

For example:

September 10 is Teachers' Day. September 10 is teachers' day.