I understand I have not understood the question right when I answered the following:
Because of inertia. If no forces are acting on an object, the objects velocity does not change. Using a string the car accelerates the object to a certain velocity and when slowing down the object will continue to move towards the car as no forces are acting on it (until it hits the car where the normal force of the mass of the car slows it down at once). Using a rod the object again accelerates with the car as it is tied to it. But when the car slows down, the normal force of the mass of the car immediately acts on the object thrue the rod, slowing down the object at the same time as the car slows down.
If I understood correctly what is meant here, the reason for the object making an angle to the "vertical" is simply inertia and the fact that it the string has a finite length: The object (attached outside of the car on the ceiling or inside on the ground) wants to stay at rest but is accelerated. The only way to stay as much at rest as possible is to move down (in addition to moving to the opposite side of the acceleration relative to the car) and thus making that angle.
If you meant horizontal instead of "vertical" (the object being attached to the back of the car outside) then the reason is chaos of aerodynamics. Aerodynamics predicts that the object moves in every direction, despite being dragged back by inertia and thus making that angle. But I'm not that familiar with aerodynamics and am therefor not able to give you more details. What I do understand is that when using a fixed rod welded to the car, the object has no degree of freedom whatsoever. Its position is completely determined by the car. A string gives the object all three degrees of freedom $(r,\theta,\varphi)$, inspite of some boundaries: $r\le L$ (length of string), $\varphi\in [0,\pi]$ (object can't go into the car), $\theta\in [0,\pi]$ (boundaries for $\theta$ are normal). Having these degrees of freedom the chaotic consequences of aerodynamics act on the object.