Also, let's say we have a population, they aren't able to interbreed with their original population, so we designate them as a new species.
Here's the reality of the situation, they all were still born of mothers. Just like in the video, if we rewind one generation and they are interbreeding, then that's the generation between old species and new.
There's really no way out of it.
The problem with your argument is that there is no category of a group that exists between two species. If species be evolves from species A, there is no in between. There is a definite point in time in which group B exists where it previously had not.
And in the video they skip generations, they jump from 200 to 1200 etc
But if we were to watch those birds, every single generation. The line between the old species and the new, it would occur at an instant in time. There's no such thing as an animal that is not one species or another and is somehow in between being either or. All animals, all individuals, are designated as one species or another.
So given that change in an instant of time, however you draw that line and whatever individuals are inside of the group or outside, regardless of when it happens, you will be left with a situation where the parents are of a different species than children.
Just like if I go to the store and I have a group of shades of black and dark gray, and I have a group of shades of white and light gray, if I have to separate white from black, I have to draw the line somewhere. And it doesn't matter who's on one side or the other or what color or what shade is on one side or the other.
At some point in time, you will have to definitively say, this is not black, this is white. In one generation, you will have to make that judgment. No matter how you want to classify species.
So even if we took your answer, and you said when all the children can no longer interbreed, that's the moment the individuals are designated as a new species, okay even if we took that, those individuals still had mothers that existed in a time before then. And so their mothers would not be part of the new species. Because there would still be interbreeding going on.
No matter how you shake it, you have to draw a line in a point of time. And that point of time is not something gradual, it's a moment. Even if the overall process is gradual, the line is still at a moment in time.