Let me try and explain it this way.
When you buy a car, you aren't keeping it forever. There will come a day when you sell it, scrap it, trade it in, whatever. So, even though you bought it, it's not like a house that you can keep "forever" that has value.
To keep it simple, let's assume that day is 10 years after owning it. You've paid your loan in full, you have whatever costs you put into it, you have tax, and then you have whatever you get back at the end. After 10 years, you have $X.X cost of owning the vehicle regardless of how you get rid of it.
Let's assume, when you average it out each month, that ends up being $300/month over the course of the 10 years. It doesn't matter where those costs went (some cars cost more at the start, less to maintain and vice versa). And it doesn't matter that your loan ends after 5 or 6 years or whatever. It's just the average cost to own.
Now, let's say I leased 3 vehicles over the same time frame and my overall cost ended up being $350/month for the same car.
The lease cost me more over 10 years. But I got some benefits for that increased cost. Is $50/month worth it to have had newer cars, no maintenance to worry about, etc? Well, for some, the answer is yes. For some, the answer is no. That's why there's no right answer to leasing vs buying except for certain circumstances.
If you drive a lot or like to keep a car 10+ years, then leasing is silly. If you are looking to change cars every 5 years, then buying is silly. Otherwise, it's more a matter of preference.
Do I buy a nice phone that costs me $20/month more because of the features it has? Well, that's up to each person. Same goes with leasing.
ETA -- Even when you buy a car, you are essentially "renting it" because of the fact its value always goes down. It's not like buying a home that you put money into it and you will likely get it back, if not more (unless we're talking about a collectible, which is not what this discussion is about). The shorter you keep it, the higher that "rent". The longer you keep the car, the lower that monthly "rent" is for the vehicle, but either way, you will almost certainly one day get rid of every car you buy. Since you don't get back what you put into it, it's money that is gone forever for the use of that car. Just like a lease