Try to prove that statement wrong: try to show that you can have 36 people, 6 of whom don't have to be born the same day of the week.
How would this work? Well, we need LESS THAN 6 people to be born every day of the week.
So: Monday: at most 5 people
Tuesday: at most 5
Sunday: at most 5.
But notice, there are 7 days in a week and at most 5 people per day, which is 35.
35 < 36 and we know if we increased any one of those days by 1, we'd be at 6 which we don't want!
It follows that there are always 6 people born the same day of the week in a group of 36.