There are at least two reasons for which you can say the Union “needed” to resupply Fort Sumter.
On one level, you can say the Union needed to resupply the fort because the fort was in Southern territory. The fort was in the harbor of Charleston, South Carolina. That meant that it could not get any supplies on its own since the South felt it was an enemy outpost. It was running out of supplies and had less than a month’s worth of provisions. Therefore, it needed to be resupplied from the North.
On another level, however, we can talk about why the North felt it needed to keep Fort Sumter. The major reason for this is that it felt to many Northerners like a point of pride. They did not want to feel as if they were giving in to the South. If they had simply let the South chase them out of Fort Sumter, they would have felt weak. For this reason, they felt that they needed to keep the fort. If they were going to keep the fort, they had to (as discussed in the previous paragraph) resupply it.