Why is there red ink on a US 2 dollar bill?

Red ink, as well as the banner across the bill's top front, indicates that it's a United States Note. US Notes were effectively the same as Federal Reserve notes except they were issued directly by the government instead of through the Federal Reserve System. To save printing costs US Notes were discontinued in the late 1960s and all subsequent bills have been issued as familiar green-seal Fed notes.

Other seal colors used during the early and mid-20th century were:

• Blue: Silver certificates, discontinued with the 1957 series.
• Gold: Gold certificates, discontinued with the 1928 series.
• Yellow: Used during WWII on special bills printed for troops serving in North Africa
• Brown: Used during WWII on special bills printed for civilian use in Hawaii