False Dichotomy of Pro (and what the real dichotomy is)
Research vs destruction is negated even on the simplest of concepts; you can do your research and destroy it after. Nonetheless, let's explore just what the two sides are and what would happen to this alien once it's born. Pro would have you let it be born to feign mercy, only to keep it trapped, probed (ironic), tortured, tested both psychologically and physically to the point it breaks or dies... Is that merciful and kind? Do you think they're going to let the alien roam freely as a wild horse would? Of course not. What is going to happen to the alien(s) once it/they is/are born is merciless and immoral.
Pro comes at you from a stance of research vs destruction but in reality not only is research less merciful post-hatching, it's also able to be done on the eggs before we destroy them. We could destroy each one in a different way as part of an experiment that gives us useful results. On top of this where is Pro deriving the 'should' from? I offer you a different dichotomy; risk vs reward.
The alien is being born on a planet its genetic pool never evolved to inhabit. Would you hatch a fish egg on land unless you were merciless? Would you hatch a bird egg under water? This alien is not supposed to be hatched in our environment, it's here by mistake and if it does somehow survive our Earthly conditions what is it going to do once hatched? Do you think it's going to be friendly and amicable? How do we know? What if it has superpowers and wipes us all out before we can blink? We know absolutely nothing about this alien entity post-hatching, it's clearly an unidentified alien egg based on what the debate's title and description leave out. We would be better off getting rid of it because while it may make us seem hostile to the aliens, what exactly is more hostile; destroying some eggs as we do with chicken eggs for food on the regular or letting them be born and using their bodies for merciless research? On top of this, the aliens are probably either very clumsy as they let eggs fall into our hands or they're extremely sophisticated and brutal, merely seeing how stupid we are and if we'd let their hatchlings grow in which case they'd telepathically communicate plans and use the beings as secret agents or something. We know hardly enough to assume hatching the eggs is safe or worth the risk.
Setting the tone for future generations regarding alien life
I hate to break it to you but you can't compare this to human migration and paint me as a right-wing bigot. I am not suggesting to be hostile to all beings wishing to amicably set foot in our land, instead I am saying that the orientation should be towards destroying these eggs unless told otherwise and here is why:
If these aliens really wanted peace with us, they'd communicate with us to ask for the eggs back. Why are the eggs being neglected? What kind of being let their young perish? If they are either cowardly or clumsy enough to do that, they are hardly going to hurt us effectively in revenge and also clearly want nothing to do with us. They'd only increase hostility with us if we were holding their beings hostage, destroying the eggs and saying 'sorry we didn't want to take the risk' is actually less likely to cause brutal retaliation than us letting this entities grow, experimenting on them and abusing them, as many lab creatures have been.
If we are to set the tone for humans regarding alien life, we are to set the tone of mirroring. To entities that do not communicate with us, we should not assume they want anything to do with us and not force integration. This is not immoral, this is sensible.