It is important to consider both sides of the argument when writing an argumentative essay. Your counterclaim and rebuttal are a great start. To further strengthen your argument, you could provide evidence to back up your claims.
For example, you could provide evidence to back up your claim that exotic animals pose a danger to people and communities. You could cite studies or news articles that discuss instances of exotic animals attacking people or causing damage to the community.
You could also provide evidence to back up your counterclaim that irresponsible owners are responsible for the attacks and invading of ecosystems. You could cite studies or news articles that discuss instances of exotic animal owners not following the proper regulations or guidelines for owning exotic animals.
Finally, you could provide evidence to back up your rebuttal that exotic pets still pose a danger in the hands of a responsible owner. You could cite studies or news articles that discuss instances of responsible exotic animal owners experiencing dangerous situations with their animals.
By providing evidence to back up your claims and counterclaims, you will be able to strengthen your argument and support your position that exotic pets should be illegal.