An experienced diver may rent a subset of their equipment, at certain points:
- Travel: Because you might want to take everything with you, due to weight/size limitations.
- Courses: Specifically, SideMount courses come to mind. SideMount can be very finicky, and people with zero SideMount experience buying a random rig will almost certainly find it doesn't work for them, and it's really easy to buy the wrong equipment. It's better to start with equipment an instructor knows works for most people and can be adjusted, and then experiment with adjustments and alternative equipment.
- Tanks: In my area, 1-day tank rentals are the same price as a tank-fill. You also don't have to maintain the tank (VIP, Hydro, etc) The down-side is you need to arrive and return during store hours. For my own diving, this often doesn't work, because I rarely control the schedule, and it's a long-drive to the nearest tank fill/rental station. Specialty tanks are also often not available.
In the medium-to-long-run you probably want to own your own equipment. However, it sounds like equipment rental where you're at may be inexpensive enough you don't need to rush to buy everything tomorrow.