In general people need to learn better aggressive interview techniques. Hostile/gotcha media has been around for at least as long as live interviews have been a concept.

You don't have to be perfectly infallible or witty. Have two or three prongs of attack, a few different phrasings, and some rejoinders or counters to their likely responses.

Don't bite with "did you just call this woman a man", pivot to a different phrasing on the same question, keep hammering and don't let them control the conversation.