You are correct that "someone" is a singular form. However, in modern English, "they/them" can be used as a gender-neutral pronoun to refer to a person whose gender is not known, or to a person who does not identify as male or female. In the sentence "If someone gives me bad advice, should I be mad at them?", "them" is used as a gender-neutral pronoun because we do not know the gender of the person who gave the bad advice. Using "him/her" would be gender-specific, and it might not accurately reflect the gender identity of the person in question. In contrast, "them" is more inclusive and acknowledges that people of all genders can give bad advice.

Use of the singular ‘they’ goes back centuries and is not related to the current issue of people having a right/obligation to choose their own pronouns. To me (I’m 61) it is much more natural than ‘he’, ‘he or she’, alternating ‘he’ and ‘she’, or ‘one’. E.g. A: Somebody called for you. B: What did they want? (The only natural pronoun here)

This problem comes up a lot when people are writing IELTS essays. Students are often reluctant to use they or them and use "he or she" and "him or her" instead. For example: A homeless person can only better their status if he or she has a bath and a change of clothes to go for an interview. If he or she cannot get help, they will continue to live on the streets, and he or she will suffer ill health and a short life expectancy. For a native speaker, it gets annoying on the third and fourth time you use the long-winded "he or she" instead of the simple word them in an essay. But it is not necessary. I checked with the British Council, which runs the IELTS test, and they say that in modern English, the pronouns they and them are perfect style and that someone can get full marks on the test using these pronouns.

But them is what tamen means

"Him" used to be used as a gender non-specific pronoun more than it is today, but you can still use it this way if you like. The reason this use of "him" has declined recently is related to the politics of gender, which in the U.S. is fraught.