Tire conicity results when tire belts are not perfectly aligned when the tire is built
Because there is more belting to one side than the other, the tire surface inflates improperly. The weaker side of the tread is pushed out slightly more than the stronger side. This results in a tire that is very slightly cone shaped, thus the name conicity.
When a cone rolls, it rolls in a circle toward the point of the cone. The same thing happens with a tire. This is why the vehicle pulls when the defective tire is placed on the front. The effect of the tire on the rear is much less, but can also cause a pull if bad enough. The above illustrations are greatly exaggerated for clarity. In reality this cannot be seen with the eye.
When the new tires are installed on the vehicle and a tire with conicity goes on the front, the effect is obvious. Less obvious is when the bad tire is originally installed on the rear. It may be several thousand miles later before the tire is rotated to the front and the problem is revealed.
Prompt action is required in bringing this condition to the attention of the tire company. Conicity is covered under the manufacturer's warranty, but quick action is best. If the tires are allowed to wear significantly, the wear may be [falsely] blamed for the pull and warranty may be much more difficult.
Tire conicity or radial pull is usually slightly different from a pull that results from improper wheel alignment. A caster or camber related pull is normally constant, regardless of vehicle speed. This is because the amount of misalignment does not change as the vehicle increases speed. When radial pull or tire conicity is the problem, the degree of the pull may increase with vehicle speed. It may be hardly noticeable at low speed and quite severe at 60 MPH or more.
Of course air pressure can cause a similar problem and tire pressure should always be verified with a precision gauge before condemning a tire. A low tire will increase rolling resistance and cause a pull.

A low tire will also cause the vehicle to lean. Since wheel alignment is based on level, a leaning vehicle will be out of proper alignment. A low tire can affect camber and cause a pull as well as tire wear.
Conicity is a well known defect in a new tire and not a problem the driver has caused. Tire manufacturers should have no problem replacing such tires as long as they are promptly and properly diagnosed.