First, let me explain about Setsubun before Mamemaki. Setsubun is now the 3rd or 4th day of February. Originally, however, it was the day that marked the end of spring, summer, fall, and winter. In other words, Setsubun was held four times a year.
However, of the four annual Setsubun days, the most important Setsubun day was the day when winter turns into spring.
In the old days, the day when winter ended and spring arrived was considered to be the beginning of the year. In other words, the bean-throwing ceremony held on the first Setsubun in February was an event that marked the end of the year in ancient Japan.
It was also believed that beans had the effect of exterminating ogres. People in ancient times believed that all illnesses were the work of demons. Therefore, people sprinkled beans in the hope that demons would not come and do bad things to them.
In other words, the Setsubun bean-throwing ceremony was a kind of old-fashioned spell to exterminate ogres on the last day of the year and welcome the new year. This tradition still survives today.