In the (very good) video game pillars of eternity 2, an imp comes to tell you his wizard wants you to see him. If you respond with “I’ll go if I have time” the imp replies “pfth. Who has time? You have to make time”. Now I think about this a lot.
I’ve also learned that sometimes when people say they don’t have time they actually mean they don’t want to, but they think a small lie is more polite. Personally if I invite you to something I’d rather you tell me you’re not interested so I know not to invite you in the future. But some people are cripplingly conflict avoidant.