Why does a tractor have different sizes of wheels in the front and back??

The rear wheels in most of the common tractors are the drive wheels and are connected to the drive shaft. The wheel turns due to the moment of the force about the point of contact at the ground and is caused by a torque applied at the axis of the drive-wheels. So a larger wheel would require less force for the same traction.
The large drive wheels offer some additional important advantages.
First, the farm tractors are meant to carry out various jobs such as ploughing of muddy fields where the traction can fail if the wheel ground grip is not substantially improved over what is available in a car tyre. Therefore, the tractor drive wheels are provided with large grip fins or pads that bite into the ground in order to enhance the grip for traction.
Secondly, the large rear wheels of the tractor fix the drivers seat at a higher elevation so as to ensure good visibility of the nose of the tractor and the corners of the field it ploughs. The apparent loss of safety from toppling is easily solved by providing a sufficiently long cross beam below the drivers seat and a longer axle of the rear wheels than that of the front wheels.
Further, the large wheels necessitate lower differential load for negotiating sharper turns essential for covering maximum area if the field while carrying out different field operations like ploughing, sowing and harvesting,