Class membership statements:

“This is one of the things that make/makes me angry.” In this sentence that make me angry is a restrictive, or defining, relative clause.  Notice that the pronoun that is used only with restrictive clauses.  It refers to the plural noun things. Likewise “I am one of the people who like to go skiing.”  If we break this complex sentence down, it translates into two simple sentences: “Some people like to go skiing.” “I am one of them.” The people who/that like to go skiing is a specific subset of all people.  But if you say “I am one of the people who likes to go skiing,” the two component simple sentences are: “I am one of the people (which people?).” “I like to go skiing.” Here the word people has no modifier, so it means people without specification.  But “people who like to go skiing” is specific and denotes a subset of all people defined by their predilection for winter sports. The rule of thumb for dropping prepositional phrases like of the people cannot be applied here without removing the defining modifier of one.  If you say “I am one…who likes to go skiing” the pronoun one just means somebody, not a member of a defined class.  It’s a semantically different case. More examples: “He is one of those people that always make/makes objections.”  “America is one of the countries which have/has freedom of the press, but not all of these countries have a First Amendment.”