Why do car manufacturers use plastic parts in the car?

Weight Reduction

Using metal components within a car to replace all of the plastic components would increase the weight and reduce the overall efficiency and gas mileage of the vehicle.

The overall energy consumption globally by replacing plastic parts with metal parts would have to be astronomical.

As @DucatiKiller said, weight is a major factor. With ever-increasing safety standards that need to be met, car weights are constantly increasing. Making as many weight savings in as many areas as possible is a major reason here. Cars are getting more efficient, with smaller engines, so the cars need to be as light as possible.

Then there's cost.

Manufacturing cast alloy products, or steel products, just isn't as cost effective as it used to be. Injection moulded parts can be made en-masse and they are cheap to produce, cheap to ship, and cheap to eventually recycle.

Also, advancements in polymers that actually make some plastics stronger than metals.

It might seem like these plastics break easily, but in a lot of cases they can perform better than their metal counterparts. They might snap if you lean on them but so might an equivalent metal part. Remember, in a modern car, it's designed to crumple like a beanie-baby on impact. Metal parts don't crush as easily in a lot of cases.

Edit: And then there's the cynical, yet very strong case of

Return customers

Oh dear, that part has broken three days outside of warranty. Isn't that conven... I mean... a pity. You best buy that bespoke, dealership-only plastic part again. See you again in a year or so!

If we made metal body, engine efficiency automatically decrease. Engine has to propell the overall if we add metal that doesn't get move or performance will decrease automatically, plastic body will be light weight so can be move easily or load doesn't act much....

There are cars that use metal in more places than most. In a Rolls-Royce, the vents are metal, for example.

But there are many places in a car where you don't want to use metals. In addition to the cost and weight issues mentioned in other answers, metal has noise issues. Esp. if you use thin sheet metal, it will readily conduct noise and vibration. That makes it undesirable to use on e.g. ventilation channels, interior panels etc.

Metal is also undesirable in places where the car's occupants will come into contact with it: e.g. the dashboard, center console, backside of the front seats. All of these would need at least some padding over it. Much more labor-intensive (and expensive) than a flexible plastic shell.

In other places, metal performs worse than plastic. A plastic bumper will spring back into shape after a minor parking accident, a metal bumper will be permanently deformed.

Plastic allows construction methods that are more difficult in metal: with injection moulding you can get parts that are thick and strong where they're needed, and thin and light where less strength is necessary. These parts can be much stronger and lighter than the equivalent made in sheet metal.
Metal casting is a process that gives results more comparable with injection moulding, but it is a far more complex and expensive process than either injection moulding or sheet metal operations.

Finally, there are plenty of cars that have durable plastic parts. I've owned several that didn't have a single part break, even when the car was 10-12 years old. It won't be hard to find a more durable car than that Twingo.