You are correct. "Someone" is singular, and the grammatically correct sentence should be "if you are sympathetic to someone who is in a bad situation, you are kind to him ...and understand his feelings." HOWEVER, the sentence as written (i.e., using the plural them/their) is how a native (American) English-speaker would say it in casual everyday speech. Why? Because Americans now prefer not to be gender-specific. If you use the singular, you must specify either the masculine he/him/his or the feminine she/her/her. Traditionally, English would use the masculine form to refer to a singular person of unspecified gender. However, with the rise of women's liberation, there is now hesitation to use "he" as the default singular pronoun. As a result, we use "they/them/their" to avoid specifying the gender, EVEN when doing so is technically grammatically incorrect when we use the plural pronoun to refer to a singular antecedent.