This episode has to do with a special dance that Beaver's dance school is putting on in which boys are required to ask one of the girls in the class to the dance. Beaver finds himself liking one of the girls in the class - a new girl who has just moved to Mayfield. He admits he thinks that he likes her just because she is new, but he has decided that he would like to ask her, so he leans on Wally for advice, and the result is endearing. I really liked how Wally helps his brother with words of wisdom about the whole situation.
Wally, having gone to dancing school when he was younger, and Beaver, now a student, seem reluctant about the whole matter of dance class - like they would not go if not made to do so. And it seems to be June who is the main proponent of their participation as she does not want them to grow up to be "crude human beings".
But the construct of Beaver's date is just bizarre. Beaver formally asks the girl over the phone to go with him, but the night of the big dance Beaver and Wally, who has been invited as a chaperon, walk out the door together - apparently this place is in walking distance - and Beaver meets the girl AT the dance. Why did he ask her to go with him as a date when he is in fact just going to see her at the dance?
The whole concept of dance class is a social construct of which I have no experience. I grew up in the 60s and early 70s, in the suburb of a big city, and I have no recollection of anybody I know going to dance class. Maybe that is because, in 1964, with the coming of the Beatles and reliable birth control and the whole counterculture movement, society just moved on from such formalities. Eating establishments needed the floorspace and so they pushed out the dancing and put in more tables. So Leave it To Beaver really does describe mores and institutions that were on their way out by the middle to late 60s. But it's all the more interesting because of that.