The David and Goliath Raid - S2-E2
Factual error: Some of Dietrich's command vehicles have license plates that begin with the letters "WL", denoting German Luftwaffe (Air Force), rather than "WH", which denotes Wehrmacht (Army), of which the Deutsche Afrika Korps were a part. Dietrich is not part of the Luftwaffe's "Ramcke Brigade" which also served in North Arfrica - he is Deutsche Afrika Korps (again, part of the regular German Army).
Suggested correction: At this point they don't have any proof that they can't kill it, and since Kirk is in danger, it's logical to try. Also, Spock is half human and he's concerned about his best friend being killed. Logical or not, he'll want Kirk to protect himself at all costs. Other episodes have shown where Spock doesn't always behave logically when his friends are at risk and he lets his emotions come out.
envisaged0ne