I’m sure they also don’t like it when you call them “transgenders”.

But, serious response, just talk to your friend about it. Do you call your friend a woman? You are a cis female, your friend is a trans female/trans woman. You are both women. If it bothers you this much, find a good time when you are both in good head spaces and say you’d like to talk about identity. Explain that being identified by that term just doesn’t sit right with you. Talk about what identifiers feel right for both of you. Be ready that this may be a tough conversation. But, it’s important to normalize talking about these things!

Some of your language could be seen as problematic here, and that’s why it’s important to talk about it. Your friend was not “born a man”, she was Assigned Male At Birth. Most people use language like this because they did not “become” whatever gender identity they are, they were born that way and were assigned a sex at birth, as we all are. Using some of this more specific language is actually done with the end goal of being more inclusive. For example, If we say “people who are pregnant” instead of “pregnant women”, we are including men, non binary individuals, etc who are also capable of becoming pregnant. Cis female is just acknowledging that you were born with a vagina, and a doctor declared you female, and you also identify yourself as female. Some people acquire their female identity through other means. Assigned Female At Birth is another common phrasing, especially among trans folks.

None of this takes away from you being a woman. Just talk to your friend.