No. You're playing into stereotyping language. The man as hunter myth.
This is not what chase means. You can't just change the definition of what words mean for reasons of ego.
Chase: 1. pursue in order to catch or catch up with. "Police chased the stolen car through the city" 2. drive or cause to go in a specified direction. "She chased him out of the house" 3. an act or pursuing someone or something [with intent to capture] "they captured the youths after a brief chase"
An approach is not a chase.
Approach: (verb) 1. come near or nearer to someone or something in distance or time. 2. speak to (someone) for the first time about something, typically with a proposal or request. "the department has been approached about funding". (noun) 1. a way of dealing with something. "We need a ehole new approach to the job" 2. an act of speaking to someone for the first time about something, typically a proposal or request. "the landowner made an approach to the developer"
This use of predatorily aligned language is one of the reasons why men won't take no for an answer. Why they believe they're so entitled to women's time and attention. And why they're always such a hot mess around dating and how to date.
We can see from the definitions above what is happening is an approach, not a chase. The man requests socializing time; he comes nearer to her in a particular way so that both parties may signal to each other their interest and proceed to evaluating fitness for mating or a relationship.
It makes no difference whether they are coming together for a hook up or a long term relationship shop. The approach, the steps, are the same.
We humans approach each other more like bower birds than squirrels, but even squirrels don't chase without rules and checks in place.
Also, humans may engage in chasing as a form of sex play and that can be quite exciting and titillating. But it's not a hunt and it never happens on that initial or first interactions unless it's a sexual assault.
You're not helping anyone or making the point you think you're making using this conflationary language.
Approach does NOT equate to chase.