Not all non-native plants become problems, but too often plants out of their natural range crowd out natives.
More seeds mean more seedlings.
Purple loosestrife and sweet clovers produce hundreds of thousands of seeds or more, per plant. By prolific seed production they quickly establish in disturbed areas, crowd or shade out other plants, gradually spreading into less disturbed areas. Exotics whose seeds easily get around tend to quickly surround. Buckthorn and honeysuckle berries are eaten by birds, which deposit undigested seeds everywhere on the fly. Tiny Siberian elm seeds ride the wind far and wide.