Beaver has volunteered to be in his class pageant, but because he was at the end of the line of kids asking to be particular animals, he got stuck being the bunny. If Beaver was only 5 or 6 and dressed up as a bunny, this would be cute, and I doubt Beaver would be quite as embarrassed by the situation. Because he is 13, he is very annoyed. The night of the school pageant comes, and Ward calls home to say he is needing to stay late at work and can't get there in time to get Beaver to the school early, as required. Thus June gets Beaver - already in his costume - a ride with Lumpy Rutherford and Wally, in his not very reliable jalopy. A breakdown on the way and a stranded Beaver ensue.
Like I said already, I don't get the hate for this episode, because for sure it's not the best thing LITB did, but it is also definitely not the worst. Most people seem to think that Beaver running around in a bunny costume at age 13 as his voice is clearly changing is what makes it ridiculous, but I think it makes it surreal. The things I do find ridiculous? The kids brought their costume to school in the morning for dress rehearsal, but are for some reason required to already be wearing it when they come to the pageant. Why? Also, Ward needs to get a second car. This isn't the first time him being at work, unable to get away, has caused a situation at home. He can afford to belong to a country club and golf every weekend, he should surely be able to afford a car so that June is not always left stranded during some crisis.