If an invasive plant species makes its way into your landscaping, you definitely want to remove it as soon as possible. Buckthorn is one invasive species that is problematic throughout Minnesota. The good news is that the seedlings can be pulled without the worry of re-sprouting. Unfortunately, this is just one of many invasive species that can be problematic.
As for why an invasive species is such an issue, it can actually crowd out and displace native plants and it is also a nuisance. In the case of Buckthorn, it creates dense thickets in yards, parks, forests, and along roadways. A plant that started out as a simple hedging material that was brought from the Europe to the United States in the 1800s escaped and became a problem. Now it has caused trees and shrubs in the mid-layer of the forest to become displaced, which has also affected the wildlife, such as birds that once nested in trees that are no longer there.