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Since the instantaneous rate of change is the rate of change at a particular point or instant in time. This is better than average rate of change because an instantaneous rate will give you the rate of the reaction at that exact instant in the reaction.
Since reaction and product concentrations follow smooth curves that are defined by equations, we can easily use the instantaneous rate of change, which will give us a more accurate result than using an average. It also allows us to turn the differential rate laws into the integrated rate laws.
The instantaneous rate applies to a specific point in time which is more useful than an average rate as the graph may not be as consistently simple in which the average rate can be very different as to what the actual rate is.
You would take the instantaneous rate over the average rate because it is more accurate since it is the rate at one specific time instead of that at an interval which would lead to a greater margin of error.
With average rate, there is a larger error because you are treating the curve as a line when taking two points into consideration. However, with instantaneous rate, you are using only one point to get the slope, which results in a more accurate slope.
An instantaneous rate provides an infinite amount of time points that you can measure the rate. It is more accurate than taking the average between two points because you are looking at the exact rate in time, rather than an approximation between two points where the rate in between the two points can be non-constant.
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