"Chasing" doesn't have to mean aggressively pursuing or wooing. It simply means showing that you're interested. If a man likes you, he will show that he likes you, by, for example, texting about those podcasts he mentioned, or arranging the next date.
It's not about enforcing rigid gender roles. Just noticing that men will show interest in women they are interested in. If he doesn't show interest, he's not interested.
There is therefore no need for you to show interest in him at this point or to ask questions of him or try to find out what he's feeling etc. All that will do is make him believe he has won you over and can pick you up and drop you whenever he pleases. He will know that you're interested in him even though he has shown you he is not interested in you, and will think this means you will be available for no-strings sex as clearly him not liking you hasn't stopped you, in his eyes, chasing him.
Of course not all men think that way. But those who are genuinely decent people do not make big plans and then drop you or ghost you. They let you know it's not working out for them and wish you well, so you know where you stand. Not doing that is not a sign that he really likes you but he's too shy or has trust issues or whatever. That's not how it works.
If you don't know where you stand with a man, it's highly likely that he has made his non-interest perfectly clear through a lack of communication, dropping out of plans, or otherwise being weird and evasive. Don't make excuses for people who do this. If he likes you, he will not act like he doesn't like you. (And if he does, then... well, that's a whole other kettle of dysfunction you don't want to get involved with.)