How can they say when either each / neither comes are in singular form?
For eg Either Anirudh or his friends [are] responsible for the class.
As a rule, either, each, neither take a singular verb after them. However when the second subject is plural, the verb must be plural. For example:
Each of the the boys in the class is punctual. (Singular subject)
Neither Sanya nor Richa is attending the class. (Singular subject)
Either Tom or his neighbours are making noise. (Plural subject)