The sentence presents a cause-and-effect relationship between language and our ability to understand different perspectives. To express this relationship correctly, we need to use a coordinating conjunction (such as "by") and a pronoun (such as "us") to convey the cause and the effect, respectively.
Option A uses the coordinating conjunction "while," which implies a contrast between two ideas, rather than a cause-and-effect relationship.
Option C uses a misplaced modifier, suggesting that the means are given to the perspectives, rather than to us.
Option D uses the subordinating conjunction "although," which suggests a contrast between two ideas rather than a cause-and-effect relationship.
Therefore, option B is the correct choice, which uses the coordinating conjunction "by" to express the cause-and-effect relationship, and the pronoun "us" to convey the effect. The sentence reads, "Language opens the door to other perspectives by giving us the means to apprehend other ways of viewing our common world and our common humanity."