He actually does.
Evolution of reptiles to mammals doesn't answer how the offsprings evolved to be dependent on their parents.
Which sort of answer can you conceive for such a question? It seems to me that several reasonable ones already exist, from "by luck of the draw" to "by things happening as they did", passing through "because they happened to speciate through environments that made such protection possible".
Evolution doesn't happen in one day night, so the offspring wouldn't be dependent on their parents in one day night,
Correct. It happened very gradually through a great many generations.
so if we accept that the offspring were gradually dependents from 0 dependent to 100% dependent,
I'm not sure those numbers are very objective in such a scenario, but let's ignore that for now.
then the question rises and which is what triggered it to go steadily in that direction and how it is favored by natural selection.
We don't know that it was steadily, although odds are good that it was at least in a general way.
It is conceivable that some specific generations or ranges of generations went the other way to a perceptible degree. Mutations
are random, after all.
It is favored by natural selection among other reasons because it is more economical. Fish lack ways of effectively protecting their offspring, and they pay a price for that; they have to lay a lot of eggs just in order to ensure the next generation. That results in considerable losses. Reptiles and mammals have considerable better options, and there are advantages in protecting their offspring - for instance, it is a more effective use of their resources, and it also results in mutual protecting, further improving the odds of survival for the species.
Natural selection is the process by which individuals with characteristics that are advantageous for reproduction in a specific environment leave more offspring in the next generation, thereby increasing the proportion of their genes in the population gene pool over time.
That is not accurate. Leaving more offspring is not always by itself advantageous for natural selection. Having capabilities and behaviors that improve the odds of the offspring surviving and reproducing by their turn is. It just turns out that as we distanced from fish into becoming mammals our numbers of offspring actually diminished, because our survival and reproduction strategies did not benefit from larger generations.