Imagine being a medium sized country. You've signed treaties, agreed to certain proposals and negotiations, that you will not try to acquire nuclear weapons. Rather, it's better to rely on the nuclear umbrella of the U.S. and her allies.
You see the fall of the USSR, and Ukraine's agreement to relinquish it's nuclear weapons, with the agreement by Russia and the U.S. that it's current borders will be honored.
You see Iran agree to the JCPOA, then that treaty get dismantled by the new president.
Fast forward to 2022, you see Russia invade Ukraine. Initially, you see a flood of support into Ukraine, and you think, "maybe, it's a good idea to trust the U.S' promises. After some time and growing domestic dissent, you see the U.S. lower it's support.
Coming to 2025, you see the president of the U.S. yelling at the leader of Ukraine, and rolling out the red carpet (literally) for Russia. You see the U.S. threaten her core allies, and if the U.S. is threatening European democracies in a land grab move, what's to say it wont do the same to you? You see the U.S. kidnap another country's leader in the middle of the night, what's to say it won't do the same to you.
Interestingly, you notice the U.S. seems to only target those countries which don't have nuclear weapons. Easy targets for a country with the strongest conventional military in the world.
You see Iran get bombed in 2025, then a full on war break out in 2026 over it's development of nuclear weapons. You see the near panic of American leaders when it comes to the prospect of Iran getting nuclear weapons. The U.S. has shown it won't defend allies. It will threaten allies. It isn't afraid of invading sovereign countries and kidnapping their leaders, if they don't have nukes. Only nukes seem like a surefire way to protect your sovereignty as a country and your rule as a leader.
Not only does it seem logical to develop nuclear weapons, it seems like a fatal mistake to not. The unipower world only works if that power fulfills it's commitments, and maintains diplomatic stability. What the U.S. is doing now is playing the realpolitik of the 1880s, where the only real currency isn't diplomatic allyships, isn't trade relationships, it's raw military power. Why wouldn't you?