why the model IS300 have different tyre sizes in front and rear

That is to go along with the look and feel that the designers wanted. The IS series is supposed to be a fast, sleek car. In order for one to associate this car with being fast, it must look like other cars built for speed. l submit NASCAR as proof.

This is because it is rear wheel drive. The tires on the drive wheels will be wider to help prevent oversteer when accelerating through a turn. Not as big of a concern on heavy or less powerful vehicles, and not as big of a problem for front wheel drive, because all the weight of the engine is on the drive wheels, so they will get better traction.

l think to make it is front end a little bit lower so that it could have more aerodynamic design.

Since it is a real wheel drive car, the tires in the back need to be thicker to improve traction. The more area surface, the better the traction and handling.

Different sized tires usually give you better traction and a more sporty feel to the car.

It is all about grib, baby. For that IS is rear wheel drive and when you get her pumpin' and going.that rear might wag. More rubber means more grip.