Basically for positive things, we use 'both' or 'neither.' For negative, we use 'either'. Though it seems like 'both' is used for plural and 'neither' isn't, they actually are used in similar ways. When saying something in a positive way "I (do) like..." then the choice is between 'both' or 'neither'. "I (do) like both of them" or "I (do) like neither of them" / "Both Marsha and Sherry are coming to the party" "Neither Marsha nor Sherry are coming to the party." They start the same way. 'Both' + 'and. 'Neither' + 'nor'. 'Either' is a special word for plurals or when you have a choice (or). It's used in a negative way "I don't like either of them" or "I'll have either the bagel or the muffin." Do you see how it replaced 'both' and 'neither'? Here are some examples -remember when I say 'positive' I mean the sentence is positive only. "I like both of them" (positive plural) = "I don't like either of them" (negative plural) = "I like neither of them" (positive plural) "I'll have both the bagel and the muffin" (positive, singular, both selected) = "I'll have either the bagel or the muffin" (positive singular, fine with any selection) = "I'll have neither the bagel nor the muffin" (positive singular, no selection)

Because "both" = two, "either" = one of the two

I am not a grammar expert, but this might help see what's kind of going on with your example sentences. Try replacing the nouns with pronouns and then make the verbs agree: "Both Mari and Anna come to a party." --> The phrase "Both Mari and Anna" can be replaced with "They", in which case you would then form the sentence: "They come to a party." This works. "Neither Mari nor Anna comes to a party." --> I can't use a pronoun to represent the group "neither Mari nor Anna". If I were to replace both with pronouns it would be "Neither her nor she comes to a party." (I'd never say this because its totally unclear who "her" and "she" is, this is just for the purpose of this exercise.) So the result is you need to use the word "comes" to agree with the word "she". Basically, I can't keep the "neither nor" form and use the word "they" anywhere. Therefore, the following verb has to be singular. As a side note, in casual conversation people don't always make the verb agree. I would be surprised if someone actually stopped to correct you for such an error. The only case it might sound a little off is when you have the pronoun "I", such as: "Neither Mari nor I are coming to the party." It should be "Neither Mari nor I am coming to the party." But usually what people say instead is "Neither of us are coming."- so that one special case doesn't even come up!

It's a fairly simple concept in English: Positives bring things together. Negatives (and questions) separate things.