Check out the example in the cropped image. Note that the sentence ends with "a great place for an engineer to make a name for themselves." Themselves is plural, but its antecedent (the word the pronoun references) is engineer, which is singular.
This practice of using a plural pronoun to reference a singular antecedent is common in speech. But it doesn't make for good writing. Pronouns and their antecedents must agree in number.
Using the singular pronoun himself once solved the issue without presenting problems. However, with changing views of gender within modern society, using himself can be viewed as sexist. Some have simply replaced himself with herself, but this selection is just as awkward in the other direction.
The writer has two options to correct the error.
Option #1: Make both the pronoun and antecedent singular.
My recommendation with this option is to use himself or herself. While some view this construction as clunky, it avoids the awkwardness felt by a female reader trying to relate to himself or a male reader trying to relate to herself. That feeling of connected inclusion is important for keeping your audience engaged. In addition to being inclusive, himself or herself agrees in number with its antecedent. Thus, applying this recommendation would produce the corrected phrase:
With this option, the writer skips the gender issue entirely. Themselves is already plural, so then making engineer plural brings the antecedent in numerical agreement with the pronoun. Applying this option produces the corrected phrase: