Your logic is wrong: Instead of setting the date's day to 1, you're adding a day to the current date.
Try something like that:
NSDate *today = [NSDate date];
NSCalendar *gregorian = [[NSCalendar alloc] initWithCalendarIdentifier:NSGregorianCalendar];
NSDateComponents *components = [gregorian components:(NSEraCalendarUnit | NSYearCalendarUnit | NSMonthCalendarUnit) fromDate:today];
components.day = 1;
NSDate *dayOneInCurrentMonth = [gregorian dateFromComponents:components];