How do you define what makes a "product?" How is it different than project? A service? Can it be more than one of those things? Or none of them? When do you need sit down with your product and discuss what it is, what it is not, and how it identifies itself. Is your product suffering from a bit of teenage angst and it will be just fine once it has time to become a little more independent? Perhaps it's suffering from a mid-life crisis? (What would the software equivalent be to buying a red convertible Ferrari and trying to be something you are not?)
As product managers and product thinkers, we can help our products become their best (software) selves. Maybe they are a service, and that's okay. And we should not be embarrassed if our product turns out to be a project instead. We should love them and nurture them whatever they may be.