Why is the drill squealing?

Friction between the machine and the part could be the source of the squealing. When a drill gets clogged up with chips, it may dissipate some of the pent up energy as high pitched noise, to your dismay. Changing drilling speed and applying oil to the drill bit or workpiece could help mitigate the chip build-up and thus the noise. If that fails, using a sharper drill bit or one with fewer flutes. If none of these options work, it may be an internal issue in the drill.