Why does NF3 have a smaller bond angle than NH3?

I've already read many answers about the reason why $\ce{NF3}$ has a smaller bond angle than $\ce{NH3}$ , but I can't seem to understand them. Here's my understanding of the situation:

1. $\ce{NH3}$: Here N is more electronegative than H so a large electron cloud is crowded over N. This will push the bond pairs $\ce{N-H}$ away from the central atom. So, the angle of $\ce{H-N-H}$ will decrease.
2. $\ce{NF3}$: Here F is more electronegative than N, so the lone pair cloud over N is scattered into the $\ce{N-F}$ bonds. Thus the smaller electron cloud over central atom is unable to push the $\ce{N-F}$ bonds away from itself as much as it did previously. So, bond angle should be higher than previous case.