Why can't we make a sterilization bomb to drop on the third world to force them to stop birthing out babies and overtaking our nations?

Can I offer my country to be the first victim?
I am assuming that you mean poor countries when you say the third world, because, you see, there is no third world until you can tell what a second world is. More on that later.
I am a Bangladeshi from Bangladesh, one of the sh*thole countries that can’t stop birthing and are overtaking your nations.
By your nations, I assume that you mean affluent and developed countries, like western Europe or norther America, who by your mistaken notion belong to a first world (I wonder where the second one is, hmmm). Nice. I know who you are and I know where you live. In a moment that would become important.
First of all, my poor little sh*thole of a homeland is very crowded.

And, that holds us back a lot, despite making some amazing progress in the last decade or so.

The population is still growing, though at a rate of 1.1% now. There are some some 147 million of us (may be even 180 million, some say) living in 147,570 km². That means a Iceland-sized country (population 300,000) is hosting a Russia-sized population (size 17.1 million km²).
In Russia, about 9 people live per km², and in Iceland about 3 people. In Bangladesh, 1,500 people live per km². 20 million more of us floating around the world.
You want to stop us from overtaking your nation? Dude, we want us to stop from overtaking our own country. We are overtaking it a little too aggressively. Much like them…

If you don’t know who they are, let me introduce you the locusts, one of the seven pestilences of Egypt, the vanguards of the wrath of Abraham’s god.
We would appreciate the sterilisation bomb very much.

You see, all of us poorer and less developed countries have been trying to sterilise our people, without much success. May be, just may be, a sterilisation bomb would do the trick. In Bangladesh we started back in 1950s, and are still not making much progress.
But there’s a small problem. You will have to make that sterilisation bomb really big. Awfully big. Because, most of the 7 billion people in the world live in those poorer and less developed countries.

And, if it is really that big as to sterilise all of us citizens of sh*tholes, then it definitely will have residues in the air. All biological bombs work that way, as well as most other bombs, if not all.
When you have sterilisation agents polluting the air like thick smog. You face the consequences.

The winds that carried you sailships across the world and back colonising and plundering us for centuries will also, quite definitely, carry the sterilisation agent. To your nations. Super-volcano eruptions have been known to do that quite efficiently, despite volcanic ash being much heavier particles than biological agents.
That is terrible, innit?
When all you population goes infertile, everywhere on earth, you will have the last human generation roaming around. Everyone Dies™ in a generation. When they depart, the entire world goes back to its pre-human party.

Almost.

P.S. Please note that the third world is an outdated and obsolete concept and and an anachronistic throwback from the Cold War era, concocted by propagandists to denote countries that are unaligned to either USA or USSR (like Switzerland), while the first world were countries aligned with the US (like Haiti) and the second world were countries aligned with USSR (like Iran).