There's a difference between a race and a religion. A race is a race, there are no leaders in a race, there are no code nor a book of guide in a race while a religion there is hence why it is called a religion. Is there anything wrong with Trump's logic? No. We're all entitled to think what is best for us, he is entitled to think what is best for his country. Do I disagree with him? Yes and no. I'm a Muslim hence why I disagree, but I don't disagree with him also because look at what has happened. Not one group, not two group, but no doubt there are close to 100 groups of terror-minded fools on this planet, if not more, who has brought nothing but pain and terror into this world, who has taken innocent life one after another for the sake of their missguided belief, for the sake of their supposed highway to heaven. Thousands, or maybe even millions of cowards who thinks that their passage to heaven is by killing innocent people because apparently in their sick demented brain that's "kindness", "the only way" and outstandingly even "good deeds". Look at Paris, people open their arms open for them and they repay them with blood. People argue that those terrorist are terrorist disguised as immigrants, not immigrants looking for better life and it may be true due to these I.D's or some sort that the authorities apparently discovered but how can anyone even tell the difference? Look at Finland, or some other parts in Europe that is dealing with criminal issues. Just a few days ago I read about a 14 year old girl raped by a 17 year old immigrant and there were more even before this latest news. They open their arms open for you and you rape their children as a repayment? I'm a Muslim, I don't argue with the contents in Quran, similar to how a lot of Christians don't argue with the contents in the Bible, it depends on how we take the contents, it depends on how we deliver in response to the contents. I read somewhere that most contents in relatence to "killing / or any barbaric actions" are based on wars, what we would do in a war, how we would operate in a war e.g if nation A is at war with nation B over some sort of conflict, soldier A is holding a gun directing it to soldier B, therefore it is only logical for soldier B to fight back in response, both for his or her life and also for their nation, the usual logic in a war. But we are not at war are we? Any Muslim with a proper function to their brain and logic would never side with any of all the terrorist in the world, regardless of the religion we believe in. Islam is not the religion of peace and never will be until the day all of us unite as one and know what is right and what is wrong, unite as one to declare that none of us are terrorist, none of us wants to kill you in the name of our religion. Contents in Quran can both be translate into peace and not peace, similar to any religion, it's all decided on the individuals who belong to the religions.
If Muslims cannot accept the difference in culture as well as belief in the Western civilization then make your way back to the Middle East, if you cannot live in peace and co-exist with people who have been in the country for generations then make your way back to the Middle East. If you want to kill innocent lives to make this world a "better place" then take the gun, shove it down your throat and pull the trigger so there will be more space for people who can co-exist, more space for China to finally abandon their 2/3-child policy.
In conclusion, no Trump's logic is not wrong. He is doing what is right in his mind for his country, similar to how you would do what is right for your family, yourself and your loved ones.