Average velocity comes from two positions. Read the tape under the car at t1 and at t2: vavg = Δx ÷ Δt, the slope of the orange secant on the x–t graph. It belongs to the whole interval, not to any one instant in it.
Instantaneous velocity is where the average settles. Press SHRINK Δt: the faded car slides back to the car at t1, the secant pivots onto the teal tangent, and vavg settles on vinst, the speedometer reading (the car only moves forward, so speed and velocity agree). Δx and Δt both shrink toward zero, but their ratio does not. The interval stops at 0.01 s, because 0 ÷ 0 is not a velocity.
Why the average runs ahead. The car speeds up the whole time, so after t1 it always moves faster than at t1: vavg stays above the speedometer reading for every Δt, and the gap shrinks with Δt.