Aliens. As long as they don't want to destroy or enslave us, or harvest our brain juices, why would discovering intelligent life mean terrible things for humanity? Well, as this Kurzgesagt video explains, it would suggest the Great Filter — a cataclysmic barrier that prevents complex life from leaving its home planet — is ahead, rather than behind us.
There's a lot of aspects to Robin Hanson's theory of the the Great Filter, but the gist is that, given the massiveness of the universe, why does Earth appear to be the only planet where life exists? If we accept this as true, then either we're incredibly lucky and dodged whatever calamity usually stops life from becoming intelligent or... we haven't hit it yet.
In the video, the ramifications of each scenario are expanded on. So, what does this have to do with finding alien life and why it would be bad? Here's why:
The more common life is in the universe and the more advanced and complex it is, the more likely it becomes that a filter is in front of us. Bacteria would be bad, small animals would be worse, intelligent life would be alarmist. Ruins of ancient alien civilisations would be horrible.
The best case scenario? Our searches on Mars, Europa and everywhere else we're looking for life turn up nothing.
Screw that. I, for one, want the opportunity to welcome our <INSERT CHOICE OF ALIEN OVERLORDS HERE>.