Ya this is true that one should not go for big and broad tyres for your car and even bike also. this is due to the fact that while designing the vehicle the vehicle manufactures develpo the suitable type of tyre for that car only and they make sure that this tyre will be best suited for that vehicle. Modifying this without knowledge may cause harm to your car in terms of fuel consumption, cars grip on the road and above all the braking system.
Forr fuel consumption- broad tyres have a large circumfrenced surface area that causes excess friction which again causes cars engine to apply more force on the vehicle thus increasing the fuel consumption
Car manufactures make the tyres surfaces design according to car design, they are made to help car grip the road. broad tyres cant do so.
Broad tyres large surface area leads to excess friction which leads braking system to apply more force thus decreases the performance.
Broad tyres only look good but are bad.