So I was watching this Khan Academy video. For explaining the patterns formed on the screen they assumed $8$ point sources and said that if the point source number $1$ interferes destructively with point source number $5$ then the rest of the waves also mutually cancel out (destructive interference). I agree with the video upto this part. But my question is : Why should we consider 8 point sources and not an odd number of point sources like (say) 9 ? If we consider $9$ point sources the explanation is no longer valid. Suppose at the shown point of the screen wave from point source $1$ interferes destructively with wave from point source $6$ then waves from point sources $2,3,4,7,8,9$ also cancel out pairwise as before. But the wave from point $5$ still remains and does not mutually cancel out with another other light wave (from another point source). So if we consider odd number of point sources the shown point on the screen should not have a dark fringe (or minima).
To sum up my queries:
Why should we take even number of point sources to explain single slit diffraction pattern ?
Is there any method to resolve this discrepancy ?