My mom's doctor says that colon cancer can not metasize to the brain without first affecting the liver. is that true?

Generally yes: With very rare exceptions, your doctor is correct. Blood draining from the colon goes through the liver first, before entering general circulation.

False: My old professor taught me that cancer does what cancer wants. Although liver metastasis is the most common and the first site, sometimes the liver will be spared as the tumor spreads to the lung especially for left sided or rectal cancers.