Why should Congress decide which territories in America can become a state? How could this lead to dissension between parts of America?

Congress does not decide the territories in America that will become states of the US.  Instead, states apply to Congress for admission into the Union, when they have met the requirements and followed the laid down processes.  The standard procedures rule out any dissensions arising between parts of America.

Explanation:

Article IV Section 3, Clause I only authorizes the US Congress to admit new states.  It does not give it any powers to create new states.  The requirements for a new state to be admitted into the US union are clearly spelled out.  Any territories or parts of the existing states that meet the requirements will certainly be admitted as states.  Conclusively, Article IV, Section 3, Clause 1 of the US Constitution states the conditions for admitting new states.

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