This is false, and you have been shown.
Rom 2:12 For as many as have sinned without the law shall also perish without law: and as many as have sinned in the law shall be judged by the law;
This verse clearly says a law is not necessary for those who have sinned to perish.
But Paul goes further and explains that men without the written law have the law written on their hearts, and also have a conscience which condemns them.
Rom 2:14 For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves.
Paul is not teaching that men without the law perish for Adam's sin, he is teaching that all men have a sense of right and wrong and are therefore accountable to God. They perish for their own sin.
The lengths that some will go to, to try to prove
their opinion is unbelievable. Context Winman! Context! Did you read a couple of verses later:
Behold, thou art called a Jew, and restest in the law, and makest thy boast of God, (Romans 2:17)
--What law is being spoken of here? What law did the Jew rest in?
It is the Mosaic law that is being spoken of and it is the Jew throughout the passage that is being addressed or at least being spoken of.
The Outline:
Chapter one: Paul demonstrates that all Gentiles fall under the condemnation of God--that they are all sinners.
Chapter two: Paul demonstrates that all Jews fall under the condemnation of God--that they are all sinners.
Chapter three: Paul demonstrates that all Jews and Gentiles fall under the condemnation of God; none are excepted; we all are sinners (Rom.3:23).
You said (taking this verse out of context):
"This verse clearly says a law is not necessary for those who have sinned to perish."
--The Mosaic Law is not necessary for those who have sinned to perish, not just any law.
Sin is a transgression of the law--God's law.
This chapter is about Mosaic Law. All sinners have broken God's law in some form--all sinners from Adam onward!