I'll share my thoughts on the original question. I think perspective and how we identify actions makes a huge difference. When I was in my early 20s I met and dated many nice men (this was in a Christian context and dating meant going for a walk or meal, or movie or church event). The key was I saw them as people. All people want to know that if they put themselves out there they won't be rejected. All people want to know that they are seen and that the other person finds them interesting. I didn't think of it as pursuing/chasing or taking the first step. What I did, if I met someone who interested me, is I'd learn about them, engage them in conversation and then make a pathway that said I was safe to talk to and welcomed their company. For example, I'd ask questions about them and their interests. If we'd been in a bible study together I'd share in the discussion. I was a history major with a specialty in reformation studies so I love to find someone who could discuss ideas. I'd let them see me as an authentic person, rather than morphing into the person I thought they'd want. If things were good I might mention some things I was looking forward to doing, or a movie I'd like to see. This let them know that I'd be open to kayaking, a walk on the beach hunting for driftwood or sea glass or visiting the Star Trek exhibit. I treated them as a person with the same shyness, or uncertainties that I might have. If they acted on it and asked if I'd like to go do one of these things with him then I'd accept. I didn't go with a laundry list of shallow items that could exclude some amazing people.
I never had a fellow feel chased/pursued by me treating him with interest in who he was. It takes a lot for a fellow to ask out a woman and making him feel safe to do so is just respectful and kind.