Native species are part of the ecosystem. All coevolved in the same place for ten thousands of years at least, maybe millions, eventually creating a structure where each piece is connected with the other and fine tuned to produce the maximum value and extract the most products from our machine.

"Non native species" is not the same term as "invasive". Lets imagine that the letter H in your black keyboard falls off. If you replace it by a blue key from other keyboard you end basically with a functional keyboard. Sometimes non native species fill a empty spot and restore a lost system functionality without affecting the other species. Sometimes they even boost the whole machine. A good example would be a native tree from the forests of Kazakhstan that is everywhere, the domestic apple tree.

Invasive species would be like replacing all the keys in your keyboard with the letter H. They turn the machine basically useless. Instead to work with the ecosystem, they destroy it, eliminate most species, and replace it by a much cheaper version. A worse system that is more simple, less stable, and has barely the minimum functionality for us to survive