"Why do you consider it impossible to accelerate Earth’s atmospheric molecules?"

You misstating the objection. It's not that it's impossible that atmosphere molecules could escape from the Earth. But rather that the quantity of escaping molecules is tiny in comparison to the total volume of earth's atmosphere and other factors- e.g. volcanoes able of bletching millions of tons of gases in a day, etc .

One of your main problems is understanding scale.

For instance a million tons in comparison to total mass of the Earth's atmosphere is tiny.

The mass of Earth's atmosphere: "Mass of atmosphere: 5.136 × 10^18 kg" Or about 5 × 10^15) tons"
http://hypertextbook.com/facts/1999/LouiseLiu.shtml

Or 5,136,000,000,000,000 tons or said differently 5.136 million billion tons.
Or a million tons is 5.136 billionth of a part of the atmosphere. Or in terms of parts per Trillion it's 194.7 parts per trillion. Or in terms of percent, it's .00000001947 of one percent.

To human scale 1 million tons is not tiny- it's huge. A fully load train with hundreds of cars wouldn't weight that much.
Or it's almost the weight of 300 Saturn V rockets which are fully fueled.

In a room 10' high by 10' wide by 10' long, there is cubic foot cardboard box in the corner. The box is a thousandth of room volume. Inside the box is a sugar cube which is a 1/2" cube, so it is 13,824th of the volume of the box and 13,824,000th of the room or 13.824 ppm of the room's total volume. Or 13,824,000 parts per Trillion.

Considering that a grain of sugar is about .5 mm in size, you would have around 15 million grains of sugar in a cube of sugar. So, a million tons of atmosphere in comparison to entire atmosphere is about same ratio that about 200 grains of sugar is to a 10' cube room- or about the same small pinch of dirt on the floor.