Also, if you think that 3 months out of 12 or so years of schooling will "abandon the kid and their future" than we should probably add years you have to go to school to minimise the effect of aggregated absence because of e.g. illness. Of course, 3 months of missed school are probably below any kind of measurability and natural and familiar influences are going to have a much higher bearing.
The kid is also probably not going to stay in a vacuum even when at home, it is definitely going to learn something on its own too. Maybe not something that will get it a better grade but most likely something rather useful in the real life.