Replacing just one tire at a time, can present challenges because the new tire will have a different tread depth and thus different accelerating, braking, and cornering behaviour. With a different thread on just one tire, the one wheel will be spinning at a slower rate compared to the others, possibly sending false signals to the traction control and antilock braking systems. These are extremely important safety systems, which need to function properly, to protect you and other passengers of the car, from car crashes that might lead to serious injuries.
Because all 4 tires spin independently of one another, our recommendation is to have them all changed at the same time, if they present significant tread depths differences. Different spinning speeds could potentially damage the drive train, and possibly affect the Tyre Pressure Measurement System of your vehicle.
As your local dealer advised you to replace just 2 tyres [TO BE AMENDED], we encourage you to follow their guidance, because they are our trained specialists. Replacing just the one tyre without changing the tyre on the opposite side of the axle at the same time, may cause an imbalance to the vehicle – potentially leading to wheel misalignment and excessive tyre wear.
If you should have a new puncture on your new tyres, after just replacing them, you should not have to change again both tyres, as the tread depth would not be significantly affected. However, you would still need to check and follow the dealers' recommendation.