Mentally disabled people in the 1930's did not have the same treatment which they are afforded today. Mentally disabled people during this era tended to be placed into mental wards--at an alarming number. Doctors during this time did not have the understanding of mental disabilities that they do today. Many hospitals were overcrowded given doctors would tend to commit the mentally disabled person (given their inability to properly treat them).
An a side note, the lobotomy became widely popular during the 1930's (in attempts to study the brain in a different way). The original study was performed on two monkeys (Becky and Lucy).
One could easily assume that George worried about Lennie being placed into an overcrowded mental facility and this is why he chose to keep Lennie with him.