Fundamentally, it's the same reasons why all balances of power have ever been maintained: because people wanted to keep the status quo. The root of the issue was of course slavery. Both the North and the South feared the other side, and by extension slavery and abolitionism, gaining control of the federal government.
The struggle was focused in the Senate because the South had a much smaller population, especially of whites. Even with the Three-Fifths Compromise, the southern states were a distinct minority in the House of Representatives. Constitutionally, therefore, the South's ability to preserve their "peculiar institution" of slavery rested with their control in the Senate. Because every state was entitled to two senators regardless of size or population, the upper chamber allowed the less populous South approximately equal power to the North.
It was thus "necessary" to preserve the balance of power in the Senate because otherwise, the slave states feared, they would be unable to prevent Northern, free, states from meddling with Southern slavery. Conversely, the Free states feared slave power, which in addition to immorality, they perceived to be a threat to Republicanism itself.
Because membership in the Senate is state based, the admission of new states into the Union posed a potential threat to this balance.
Hence why both the Missouri Compromise and the Compromise of 1850 aimed to preserve a balance of free and slave states in the Senate, typically by arranging for paired admissions of free and slave states.