Why do doctors scrub up before an operation since they cover up with gloves anyway?

If they didn't scrub up then their dirty hands would pass germs in or on the sterile gloves.

Gowns and gloves can tear or puncture during surgery. Scrubbing greatly helps reduce the risk of infecting the wound in such a case, though it is impossible to truly sterilize the skin.

There are minor sterile procedures where standard practice only requires donning sterile gloves without scrubbing one's hands first. Examples: Insertion of urinary catheters, insertion of central lines, spinal taps, etc.